Question

One number is 7 more than another. The difference between their squares is 161. What are their numbers?

Answer 1

Hello,

Let's assume a the greatest number and b the smallest.

a-b=7
a²-b²=161==>(a-b)(a+b)=161==>a+b=161/7==>a+b=23

a+b=23
a-b=7
==>2a=30==>a=15 and b=15-7=8
Proof:
15²-8²=225-64=161

Answer 2

x-first number
y-second number
Assumption:
x>y
Equations:
x=y+7
x^2-y^2=161

Put x from first equation to second:
(y+7)^2-y^2=161
y^2+14y+49-y^2=161
14y+49=161
14y=161-49
14y=112
y=8, so x=y+7=15

The solution is a pair of values: 8 and 15.