Question

The sum of the squares of two positive is 208 if the square of the larger number is is 18 time smaller number find the number

Answer 1

let two +be integers be x,y
acco to question

X^2+Y^2=208 (1)
X^2=18Y (2)

PUT 1 IN 2 WE GET

Y^2+18Y=208
Y^2+18Y^2-208=0
Y^2+26Y-8Y-208=0
Y(Y+26)-8(Y+26)=0
Y-8=0 or Y+26=0
Y=8
Y=-26(which is not possible as question says positive)
therefore Y=8

Answer 2

Let x be the smaller number.

So, the square of larger number = 18x

A/C,

Square of smaller number + Square of larger number = 208

$\longrightarrow$$\sf\red{ {x}^{2} + 18x = 208}$

$\longrightarrow$$\sf\red{{x}^{2} + 18x - 208 = 0}$

$\longrightarrow$$\sf\red{{x}^{2} + 26x - 8x - 208 = 0}$

$\longrightarrow$$\sf\red{x(x + 26) - 8(x + 26) = 0}$

$\longrightarrow$$\sf\red{(x + 26)(x - 8) = 0}$

$\longrightarrow$$\sf\red{x = 8, x = - 26}$

As x is a positive integer, x ≠ -26 ,so x = 8

$\longrightarrow$ Smaller number = 8 and

Larger number = √18×8 = 12