Question

If Asquare+Bsquare=16,and 2Ab=8. Find the possible values of A and B

Answer 1

a^2 + b^2 = 16
2ab = 8

(a+b)^2 = 24

so, a and b will not be integers. Their sum is √24 or -√24, and both will have the same sign, since ab > 0.

b = 4/a, so we have

a^2 + 16/a^2 = 16
a^4 - 16a^2 + 16 = 0
a = ±2√(2±√3)
b = ±(√3±2)√(2±√3)