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Recent questions tagged inequality


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Let $a, b, c$ be positive real numbers. Show that $$ \frac{a^{2}}{b^{2}}+\frac{b^{2}}{c^{2}}+\frac{c^{2}}{a^{2}} \geq \frac{b}{a}+\frac{c}{b}+\frac{a}{c} $$

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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
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Let $a$ and $b$ be positive real numbers. Show that $$ \frac{1}{a b} \geq \frac{4}{(a+b)^{2}} $$
1 answer 74 views
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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 $a, b$.
1 answer 48 views
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For positive reals $a, b, c$, show that $$ \frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b} \geq 3 . $$
1 answer 66 views
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Let $a$ and $b$ be positive real numbers. Show that $$ \frac{a}{b}+\frac{b}{a} \geq 2 $$
1 answer 60 views
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 $$ \frac{a}{b}+\frac{b}{a} \geq 2 $$ ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics May 31, 2021
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Solve the following absolute value inequality. $$ |5 x-3| \geq-1 $$
0 answers 32 views
Solve the following absolute value inequality. $$ |5 x-3| \geq-1 $$Solve the following absolute value inequality. $$ |5 x-3| \geq-1 $$ ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics May 30, 2021
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Solve the following rational inequality. Write the solution set in interval notation. $$ \frac{x+9}{x-6} \leq 0 $$
0 answers 81 views
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Solve the following quadratic inequality. Write the solution set in interval notation. $$ x^{2}-2 x-35<0 $$
1 answer 94 views
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Solve the following inequality. Write the solution set in interval notation. $$ 2 \geq \frac{5-3 x}{4}>-3 $$
1 answer 69 views
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Solve the following inequality. Write the solution set in interval notation. $$ 2 x+1 \leq 3 x-2 $$
1 answer 273 views
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Show that \begin{equation} \| x + y \| \geq | \| x | | - \| y \| | \end{equation}
0 answers 44 views
Show that \begin{equation} \| x + y \| \geq | \| x | | - \| y \| | \end{equation}Show that \begin{equation} &nbsp;&nbsp;\| x + y \| \geq | \| x | | - \| y \| | &nbsp;&nbsp;&nbsp;\end{equation} ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics May 21, 2021
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Solve for the variable, correct to 1 decimal place where necessary: $-a-21 \leq-2 a^{2}$
0 answers 52 views
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Solve for the variable, correct to 1 decimal place where necessary: $2 x(x+1)+3=\left(x^{2}+x\right)^{2}$
0 answers 53 views
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Solve for the variable, correct to 1 decimal place where necessary: $\sqrt{2 p-6}=p-3$
1 answer 77 views
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Solve for the variable, correct to 1 decimal place where necessary: $m(2 m-1)=5$
0 answers 57 views
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: $m(2 m-1)=5$ ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics May 19, 2021
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Solve for $x$ in $\frac{2}{a+1}-\frac{1}{3} \leq 5$ (represent your final answer in interval notation)
0 answers 60 views
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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.
1 answer 73 views
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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.
1 answer 76 views
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Suppose that $f(z)=x^{2}-y^{2}-2 y+i(2 x-2 x y)$, where $z=x+i y$.
1 answer 54 views
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 ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 10, 2021
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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 $(|x|-|y|)^{2} \geq 0$. ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 10, 2021
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What is the Cauchy-Schwartz inequality useful for in mathematics?
1 answer 40 views
What is the Cauchy-Schwartz inequality useful for in mathematics?What is the Cauchy-Schwartz inequality useful for in mathematics? ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 8, 2021
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What does the Aristarchus's inequality state?
1 answer 89 views
What does the Aristarchus's inequality state?What does the Aristarchus's inequality state? ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics May 4, 2021
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