Question

The sum of the squares of two positive integers is 208. If the square of the

larger number is 18 times the smaller number, find the numbers​.​

Answer 1

Explanation:

Let the smaller number be x. Then,

Square of larger number = 18x

Square of the smaller number = x2

Therefore,

x2+18x=208

x2+18x−208=0

(x+26)(x−8)=0

x=8,−26

But, the numbers are positive.

So, x=8

Hence, the numbers are 8 and 12.

hope it will help u ❤️❤️

Answer 2

let larger number be 'x' and the smaller number be 'y'

given that, x² + y² = 208

and x² = 18y

substitute x in

x² + y² = 208

18y + y² = 208

y² + 18y - 208 = 0

(y+26)(y-8) = 0

y = 8 since the numbers are positive.

x² = 18 × 8

x² = 144

x = 12

the numbers are 12 and 8