Question

Find two numbers whose ratio is 4 to 3 and are such that the sum of their squares is 100.

Answer 1

8 and 6 which squares at 64 and 36 to have a sum of 100.& I can't think of any others. .

Answer 2

(x/y)=(4/3)
x^2+y^2=100
x=4y/3
(4y/3)^2+y^2=100
(16y^2)/9+y^2=100
y^2(16/9+1)=100
y^2=36
y=6 or y=-6
Plugging back into the equation x/y=4/3
x/6=4/3
x=8
or
x/-6=4/3
x=-8
So there are two sets of numbers that satisfy the parameters. 6 and 8, or -6 and -8.