Question

If a+b=12 and a−b = 8, what is the value of a^2+b^2?

Answer 1

a = 10, b = 2

a^2+b^2 = 100+4 = 104


Work:
Split 12 into two even halves: 6 and 6
Increase one side by 4 and decrease the other side by 4, to make them 8 apart.
Now we have 10 and 2.

Answer 2

Explanation:

A2 + b2 = (a +b) (a-b)

Putting values

a2 +. b2 = (12)(8)

a2 + b2 = 96