Question

Two natural numbers differ by 4 and the sum of their squares is 58 find the numbers?

Answer 1

The firs number: a
The second number: b

a-b=4
a²+b²=58
Lets write b+4 instead of a.

(b+4)² + b² = 58
b²+8b+16+b²=58
2b²+8b+16=58
2b²+8b-42=0
b²+4b-21=0
(b+7).(b-3)=0

b=-7 or b=3

But, b can't equal to -7 because these number are naturel numbers. It must be positive.

b=3
for b=3; a-3=4; a=7