Question

(a^2-b^2) = 27 and (a^2+b^2) = 13 then find ab?

Answer 1

Step-by-step explanation:

a²-b²=13. a²+b²=27

(a+b)(a-b)=13

(a+b)²(a-b)²=13²

(a²+b²+2ab)(a²+b²-2ab)=13²

(27+2ab)(27-2ab)=13²

27²-(2ab)²=13²

(2ab)²=27²-13²

(2ab)²=(27+13)(27-13)

(2ab)²=(40)(14)

=4×5×2×2×7

=4²×35

2ab=√4²×35

2ab=4√35

ab=2√35