Geometric Mean

Let $A_1$ and $A_2$ be two arithmetic means and $G_1, G_2$ and $G_3$ be three geometric means of two distinct positive numbers. Then $G_1^4+G_2^4+G_3^4+G_1^2{G}_3^2$ is equal to

If $\frac{{\left(\sqrt{a}\right)}^{\left(n+2\right)}+{\left(\sqrt{b}\right)}^{\left(n+2\right)}}{{\left(\sqrt{a}\right)}^n+{\left(\sqrt{b}\right)}^n}$ is geometric mean between $a$ and $b\left(a,b>0\right)$ and $a\ne b$, then $n$ is

The arithmetic mean of two numbers is $30$ and geometric mean is $24$ find the two number

Four geometric means between $4$and $972$are _____.

Let $a,b$ be distinct positive real numbers, whose geometric mean equals $\frac{a^{t-99}+b^{t-99}}{a^{t-100}+b^{t-100}}$. Then $t$ must equal

Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4.$ Then, $x$ and $y$ are the roots of

Marks of a student in Maths and science is $147$ and $192$ out of $200$. Find the geometric mean of the marks obtained by student.

What is the geometric mean of $4$ and $16$?

Find the geometric mean of $4$ and $3$.

If $\frac{a^{n-\frac{1}{2}}+b^{n-\frac{1}{2}}}{a^{n+\frac{1}{2}}+b^{n+\frac{1}{2}}}$ is geometric mean of $\frac{1}{a}, \frac{1}{b}\left(a\ne b\right),$ then the quadratic equation $b{x}^2+nx+b=0$ has

If $n$ geometric means be inserted between $a$ and $b$ then their product is 

If $g_1$ and $g_2$ be the two geometric means between two positive numbers $a$ and $b$, then $\frac{g_1^2}{g_2}+\frac{g_2^2}{g_1}$ is equal to

If $b$ is the $G.M$ of  $a$ and $c$, then $\frac{1}{b-a}+\frac{1}{b-c}=$

If $\mathrm{G}$ be the geometric mean of $x$ and $y$, then  $\frac{1}{{\mathrm{G}}^2-x^2}+\frac{1}{{\mathrm{G}}^2-y^2}=$

The two geometric means between the numbers $1$ and $64$ are
 

If $g_1$ and $g_{\mathit{2}}$ be the two geometric means between two positive numbers $p$ and $q$, then $g_{\mathit{1}}{g}_2$ is equal to
 

If A.M. and G.M. of $x$ and $y$ are in the ratio $p:q$, then $x:y$ is 

If the A.M. is twice the G.M. of the numbers $a$ and $b\mathit{,}$ then $\frac{a}{b}$ will be equal to

Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4$. Then $x$ and $y$ are the roots of

If the A.M. and G.M. of roots of a quadratic equations are $8$ and $5$, respectively, then the quadratic equation will be