# Recent questions tagged inequality

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Let $a, b, c$ be positive real numbers. Show that $$\frac{a^{2}}{b^{2}}+\frac{b^{2}}{c^{2}}+\frac{c^{2}}{a^{2}} \geq \frac{b}{a}+\frac{c}{b}+\frac{a}{c}$$
Let $a, b, c$ be positive real numbers. Show that $$\frac{a^{2}}{b^{2}}+\frac{b^{2}}{c^{2}}+\frac{c^{2}}{a^{2}} \geq \frac{b}{a}+\frac{c}{b}+\frac{a}{c}$$Let $a, b, c$ be positive real numbers. Show that $$\frac{a^{2}}{b^{2}}+\frac{b^{2}}{c^{2}}+\frac{c^{2}}{a^{2}} \geq \frac{b}{a}+\frac{c}{b}+\frac{a} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let a, b, c be positive real numbers. Show that$$ a^{3}+b^{3}+c^{3} \geq a^{2} b+b^{2} c+c^{2} a . $$1 answer 49 views Let a, b, c be positive real numbers. Show that$$ a^{3}+b^{3}+c^{3} \geq a^{2} b+b^{2} c+c^{2} a . $$Let a, b, c be positive real numbers. Show that$$ a^{3}+b^{3}+c^{3} \geq a^{2} b+b^{2} c+c^{2} a . $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let a and b be positive real numbers. Show that$$ \frac{1}{a b} \geq \frac{4}{(a+b)^{2}} $$1 answer 74 views Let a and b be positive real numbers. Show that$$ \frac{1}{a b} \geq \frac{4}{(a+b)^{2}} $$Let a and b be positive real numbers. Show that$$ \frac{1}{a b} \geq \frac{4}{(a+b)^{2}} $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Show that for positive reals x, y, z we have$$ \left(x^{2} y+y^{2} z+z^{2} x\right)\left(x y^{2}+y z^{2}+z x^{2}\right) \geq 9 x^{2} y^{2} z^{2} . $$1 answer 64 views Show that for positive reals x, y, z we have$$ \left(x^{2} y+y^{2} z+z^{2} x\right)\left(x y^{2}+y z^{2}+z x^{2}\right) \geq 9 x^{2} y^{2} z^{2} . $$Show that for positive reals x, y, z we have$$ \left(x^{2} y+y^{2} z+z^{2} x\right)\left(x y^{2}+y z^{2}+z x^{2}\right) \geq 9 x^{2} y^{2} z^{2} . ...
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Show that $\left(1+a^{2}\right)\left(1+b^{2}\right) \geq 4 a b$ for positive reals $a, b$.
Show that $\left(1+a^{2}\right)\left(1+b^{2}\right) \geq 4 a b$ for positive reals $a, b$.Show that $\left(1+a^{2}\right)\left(1+b^{2}\right) \geq 4 a b$ for positive reals $a, b$. ...
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For positive reals $a, b, c$, show that $$\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b} \geq 3 .$$
For positive reals $a, b, c$, show that $$\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b} \geq 3 .$$For positive reals $a, b, c$, show that $$\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b} \geq 3 .$$ ...
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Let $a$ and $b$ be positive real numbers. Show that $$\frac{a}{b}+\frac{b}{a} \geq 2$$
Let $a$ and $b$ be positive real numbers. Show that $$\frac{a}{b}+\frac{b}{a} \geq 2$$Let $a$ and $b$ be positive real numbers. Show that $$\frac{a}{b}+\frac{b}{a} \geq 2$$ ...
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Solve the following absolute value inequality. $$|5 x-3| \geq-1$$
Solve the following absolute value inequality. $$|5 x-3| \geq-1$$Solve the following absolute value inequality. $$|5 x-3| \geq-1$$ ...
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Solve the following rational inequality. Write the solution set in interval notation. $$\frac{x+9}{x-6} \leq 0$$
Solve the following rational inequality. Write the solution set in interval notation. $$\frac{x+9}{x-6} \leq 0$$Solve the following rational inequality. Write the solution set in interval notation. $$\frac{x+9}{x-6} \leq 0$$ ...
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Solve the following quadratic inequality. Write the solution set in interval notation. $$x^{2}-2 x-35<0$$
Solve the following quadratic inequality. Write the solution set in interval notation. $$x^{2}-2 x-35<0$$Solve the following quadratic inequality. Write the solution set in interval notation. $$x^{2}-2 x-35&lt;0$$ ...
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Solve the following inequality. Write the solution set in interval notation. $$2 \geq \frac{5-3 x}{4}>-3$$
Solve the following inequality. Write the solution set in interval notation. $$2 \geq \frac{5-3 x}{4}>-3$$Solve the following inequality. Write the solution set in interval notation. $$2 \geq \frac{5-3 x}{4}&gt;-3$$ ...
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Solve the following inequality. Write the solution set in interval notation. $$2 x+1 \leq 3 x-2$$
Solve the following inequality. Write the solution set in interval notation. $$2 x+1 \leq 3 x-2$$Solve the following inequality. Write the solution set in interval notation. $$2 x+1 \leq 3 x-2$$ ...
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Show that $$\| x + y \| \geq | \| x | | - \| y \| |$$
Show that $$\| x + y \| \geq | \| x | | - \| y \| |$$Show that $$&nbsp;&nbsp;\| x + y \| \geq | \| x | | - \| y \| | &nbsp;&nbsp;&nbsp;$$ ...
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Solve for the variable, correct to 1 decimal place where necessary: $-a-21 \leq-2 a^{2}$
Solve for the variable, correct to 1 decimal place where necessary: $-a-21 \leq-2 a^{2}$Solve for the variable, correct to 1 decimal place where necessary: $-a-21 \leq-2 a^{2}$ ...
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Solve for the variable, correct to 1 decimal place where necessary: $2 x(x+1)+3=\left(x^{2}+x\right)^{2}$
Solve for the variable, correct to 1 decimal place where necessary: $2 x(x+1)+3=\left(x^{2}+x\right)^{2}$Solve for the variable, correct to 1 decimal place where necessary: $2 x(x+1)+3=\left(x^{2}+x\right)^{2}$ ...
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Solve for the variable, correct to 1 decimal place where necessary: $\sqrt{2 p-6}=p-3$
Solve for the variable, correct to 1 decimal place where necessary: $\sqrt{2 p-6}=p-3$Solve for the variable, correct to 1 decimal place where necessary: $\sqrt{2 p-6}=p-3$ ...
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Solve for the variable, correct to 1 decimal place where necessary: $m(2 m-1)=5$
Solve for the variable, correct to 1 decimal place where necessary: $m(2 m-1)=5$Solve for the variable, correct to 1 decimal place where necessary: $m(2 m-1)=5$ ...
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Solve for $x$ in $\frac{2}{a+1}-\frac{1}{3} \leq 5$ (represent your final answer in interval notation)
Solve for $x$ in $\frac{2}{a+1}-\frac{1}{3} \leq 5$ (represent your final answer in interval notation)Solve for $x$ in $\dfrac{2}{a+1}-\dfrac{1}{3} \leq 5$ (represent your final answer in interval notation) ...
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Solve the inequality $2-x \leq 2 x-1<11$, giving the answer in the form $a \leq x<b$, where $a$ and $b$ are integers.
Solve the inequality $2-x \leq 2 x-1<11$, giving the answer in the form $a \leq x<b$, where $a$ and $b$ are integers.Solve the inequality $2-x \leq 2 x-1&lt;11$, giving the answer in the form $a \leq x&lt;b$, where $a$ and $b$ are integers. ...
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Given: $-4 \leq-\frac{1}{2} m<5$ where $m \in R$, solve for $m$, write the answer in interval notation.
Given: $-4 \leq-\frac{1}{2} m<5$ where $m \in R$, solve for $m$, write the answer in interval notation.Given: $-4 \leq-\frac{1}{2} m&lt;5$ where $m \in R$, solve for $m$, write the answer in interval notation. ...
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Suppose that $f(z)=x^{2}-y^{2}-2 y+i(2 x-2 x y)$, where $z=x+i y$.
Suppose that $f(z)=x^{2}-y^{2}-2 y+i(2 x-2 x y)$, where $z=x+i y$.Suppose that $f(z)=x^{2}-y^{2}-2 y+i(2 x-2 x y)$, where $z=x+i y$. Use the expressions  x=\frac{z+\bar{z}}{2} \quad \text { and } \quad y=\frac{z-\b ...
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Write the following functions $f(z)$ in the forms $f(z)=u(x, y)+i v(x, y)$ under Cartesian coordinates with $u(x, y)=\operatorname{Re}(f(z))$ and $v(x, y)=\operatorname{Im}(f(z))$ :Write the following functions $f(z)$ in the forms $f(z)=u(x, y)+i v(x, y)$ under Cartesian coordinates with $u(x, y)=\operatorname{Re}(f(z))$ and $v(x ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Verify that$\sqrt{2}|z| \geq|\operatorname{Re} z|+|\operatorname{Im} z|$. 1 answer 79 views Verify that$\sqrt{2}|z| \geq|\operatorname{Re} z|+|\operatorname{Im} z|$.Verify that$\sqrt{2}|z| \geq|\operatorname{Re} z|+|\operatorname{Im} z|$. Hint: Reduce this inequality to$(|x|-|y|)^{2} \geq 0\$. ...
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What is the Cauchy-Schwartz inequality useful for in mathematics?