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

let the numbers be x,y (x>y)
here x2=18y
according to the problem
x2+y2=208....................(1)
18y+y2=208
y2+18y-208=0
y2+26y-8y-208=0
y(y+26)-8(y+26)=0
(y+26)(y-8)=0
as the numbers are +ve
y-8=0
y=8
substitute y in (1)
x2+(8)2=208
x2+64=208
x2=208-64
x2=144
x=12
the numbers are 12,8

Answer 2

Let the numbers be x,y (x>y)
here x2=18y
according to the problem
x2+y2=208....................(1)
18y+y2=208
y2+18y-208=0
y2+26y-8y-208=0
y(y+26)-8(y+26)=0
(y+26)(y-8)=0
as the numbers are +ve
y-8=0
y=8
substitute y in (1)
x2+(8)2=208
x2+64=208
x2=208-64
x2=144
x=12

The Numbers Are 12 & 8.