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Recent questions tagged inequality


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Find $x$ and $y$ if $u=(x+y, x-3)$ is the zero vector.
1 answer 46 views
Find $x$ and $y$ if $u=(x+y, x-3)$ is the zero vector.Find $x$ and $y$ if $u=(x+y, x-3)$ is the zero vector. ...
by Maths Genie Bronze Status
(5,290 points)
asked in Mathematics Aug 9, 2021
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Find $x$ and $y$ if $(x, 3)=(2, x+y)$.
1 answer 28 views
Find $x$ and $y$ if $(x, 3)=(2, x+y)$.Find $x$ and $y$ if $(x, 3)=(2, x+y)$. ...
by Maths Genie Bronze Status
(5,290 points)
asked in Mathematics Aug 9, 2021
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Prove that $A(B C)=(A B) C$.
0 answers 28 views
Prove that $A(B C)=(A B) C$.\begin{equation} \text { If } A=\left\begin{array}{ll} 2 & 6 \\ 7 & 2 \end{array}\right B=\left\begin{array}{cc} -3 & 5 \\ 0 & 8 \e ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jul 24, 2021
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Solve the system, if a is some real number:
1 answer 37 views
Solve the system, if a is some real number:Solve the system, if a is some real number: $$ \begin{aligned} &a x+y=1 \\ &x+a y=1 \end{aligned} $$ ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jul 22, 2021
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If $a$ and $b$ are real numbers, solve the following equation: $(a+2) x-b=-2+(a+b) x$
1 answer 50 views
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$5 x+2(x+7)=14 x-7 .$ Find $x$
1 answer 35 views
$5 x+2(x+7)=14 x-7 .$ Find $x$$5 x+2(x+7)=14 x-7 .$ Find $x$ ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jul 22, 2021
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What is the value of $x$?
0 answers 45 views
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What is the value of $x$? What is the value of $x$? ...
by Edzai Zvobwo Bronze Status
(8,796 points)
asked in Mathematics Jun 26, 2021
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Solve for $x$ in $\frac{5}{x}+\frac{1}{x}=\frac{2}{x}+2$
1 answer 51 views
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Show that $5.2^{x}+3.2^{x+2}=17.2^{x}$, hence solve $5.2^{x}+3.2^{x+2}=68$
1 answer 52 views
Show that $5.2^{x}+3.2^{x+2}=17.2^{x}$, hence solve $5.2^{x}+3.2^{x+2}=68$Show that $5.2^{x}+3.2^{x+2}=17.2^{x}$, hence solve $5.2^{x}+3.2^{x+2}=68$ ...
by Student SIlver Status
(10,386 points)
asked in Mathematics Jun 14, 2021
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Solve for $x$ : $\quad 2^{x}=\frac{1}{16}$
1 answer 44 views
Solve for $x$ : $\quad 2^{x}=\frac{1}{16}$Solve for $x$ : $\quad 2^{x}=\dfrac{1}{16}$ ...
by Student SIlver Status
(10,386 points)
asked in Mathematics Jun 14, 2021
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If $x$ is real, the maximum value of $\dfrac{3 x^{2}+9 x+17}{3 x^{2}+9 x+7}$ is
1 answer 61 views
If $x$ is real, the maximum value of $\dfrac{3 x^{2}+9 x+17}{3 x^{2}+9 x+7}$ isIf $x$ is real, the maximum value of $\dfrac{3 x^{2}+9 x+17}{3 x^{2}+9 x+7}$ is 1) $1 / 4$ 2) 41 3) 1 4) $17 / 7$ ...
by Student SIlver Status
(10,386 points)
asked in Mathematics Jun 12, 2021
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If $x$ is real, the maximum value of $\frac{3 x^{2}+9 x+17}{3 x^{2}+9 x+7}$ is
1 answer 75 views
If $x$ is real, the maximum value of $\frac{3 x^{2}+9 x+17}{3 x^{2}+9 x+7}$ isIf $x$ is real, the maximum value of $\frac{3 x^{2}+9 x+17}{3 x^{2}+9 x+7}$ is 1) $1 / 4$ 2) 41 3) 1 4) $17 / 7$ ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics Jun 9, 2021
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If $a, b, c$ are distinct +ve real numbers and $a^{2}+b^{2}+c^{2}=1$ then $a b+b c+c a$ is
1 answer 69 views
If $a, b, c$ are distinct +ve real numbers and $a^{2}+b^{2}+c^{2}=1$ then $a b+b c+c a$ isIf $a, b, c$ are distinct +ve real numbers and $a^{2}+b^{2}+c^{2}=1$ then $a b+b c+c a$ is 1) less than 1 2) equal to 1 3) greater than 1 4) any real ...
by MathsGee Platinum
(102,810 points)
asked in Mathematics Jun 9, 2021
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Let $a, b, c$ be positive real numbers such that $a b c=1$. Prove that
0 answers 85 views
Let $a, b, c$ be positive real numbers such that $a b c=1$. Prove thatLet $a, b, c$ be positive real numbers such that $a b c=1$. Prove that $$ \frac{b+c}{\sqrt{a}}+\frac{a+c}{\sqrt{b}}+\frac{b+a}{\sqrt{c}} \geq \sqrt{a} ...
by Pieter SIlver Status
(17,435 points)
asked in Mathematics May 31, 2021
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Given 3 positive reals $a, b$ and $c$ such that $a+b+c=1$, show that $a^{a} b^{b} c^{c}+a^{b} b^{c} c^{a}+a^{c} b^{a} c^{b} \leq 1$.
0 answers 57 views
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Let $x$ and $y$ be positive real numbers satisfying $x^{3}+y^{3}=x-y$. Show that $$ x^{2}+4 y^{2}<1 $$
0 answers 58 views
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Given 3 positive reals $a, b$ and $c_{,}$ show that $$ \frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2} $$
1 answer 53 views
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Let $a$ and $b$ be positive real numbers. Show that $$ \frac{1}{a}+\frac{1}{b} \geq \frac{4}{a+b} $$
0 answers 53 views
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Let $a, b$ and $c$ be positive real numbers. Show that $$ (a+b+c)(a b+b c+c a) \geq 9 a b c . $$
0 answers 63 views
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If $x$ and $y$ are positive real numbers, what is the minimum value of $$ (2 x+3 y)\left(\frac{8}{x}+\frac{3}{y}\right) ? $$
0 answers 57 views
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Find all positive real solutions $(a, b, c, d)$ to the following system of equations: $$ a+b+c+d=12, a b c d=27+a b+a c+a d+b c+b d+c d . $$

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Find all pairs of positive real numbers such that $a^{3}+b^{3}+1=3 a b$.
1 answer 74 views
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For all positive real values $a, b, c$, prove that $$ \frac{a^{2}}{b}+\frac{b^{2}}{c}+\frac{c^{2}}{d}+\frac{d^{2}}{a} \geq a+b+c+d . $$
1 answer 89 views
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Let $a>b$ be positive real numbers. What is the minimum value of $$ a+\frac{1}{b(a-b)} ? $$
1 answer 174 views
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If $x, y, z$ are positive real numbers satisfying $x y z=32$, find the minimum value of $$ x^{2}+4 x y+4 y^{2}+2 z^{2} . $$
0 answers 77 views
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