Question

The sum of the squares of two positive integers is 208. if the square of the larger number is 18times the smaller number, then what is the difference of the larger and smaller number?

Answer 1

let smaller be x
larger = 18x
(x+18)^2 = 208
x^2 + 324 +36x = 208
x^2+36x+324-208 = 0
x^2 +36x +116 = 0

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

Smaller number = 8 andLarger number = √18×8 = 12