Question

The H.M. two number is $\frac{16}{5}$ their $A.M$ is and $G.M$. Is $G$. If $2A+G^2=26$, then find the numbers ?

Answer 1

LET THE NUMBERS BE X AND Y.

$\frac{2XY}{X+Y}=\frac{16}{5}$

$10XY=16(X+Y)$

$XY=16\frac{(X+Y)}{10}$------(1)

A.M-

$\frac{X+Y}{2}=a$

$(X+Y)=2a$-------(2)

G.M

$g=\sqrt{XY}$

$g^2=XY$--------(3)

PUTTING (1),(2),(3) IN THE GIVEN EQUATION

$X+Y+XY=26$

$X+Y+16\frac{(X+Y)}{10}=26$

We get $X+Y=10$ AND SO $XY=16$

SO $X=\frac{16}{Y}$

$\frac{16}{Y}+Y=10$

$Y^2-10Y+16=0$

$(Y-8)(Y-2)=0$

$Y=8,2$

$X=2,8$

NUMBERS ARE 2 & 8