Question

the sum of the squares of two positive integer is 208. if the square of the larger number is 18 times the smaller number find the numbers.

Answer 1

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

so according to question 

x² + y² =  208   . . . . . . i

y² =18x²  . . .  . . . ii

using i and ii

we get 

x² + 18x² - 208 = 0

⇒ x² + 26x - 8x - 208 = 0

⇒ (x + 26)(x - 8) = 0

so x =  8  or - 26

so x = 8

neglecting negative value

so y = √(208 - 64)

⇒ y = 12 or - 12 

so y = 12  

neglecting negative value

so 

smaller number is 8 and larger number is 12 ANSWER

Answer 2

n²+t²=208
n²=18t²
t²+18t²=208
t²+18t²+81=208+81
(t+9)²=289
t+9=√289=17
t=17-9=8
n²+64=208
n²=144
n=12
numbers=8,12