Question

if a= 2-√5/2+√5 and b= 2+√5/2-√5 find a^2 - b^2. Plz give me answer fast i will select u as abrainliest one thnx so much i need the solution thnx

Answer 1

Rationalize the denominators of a and b.

$a=\frac{2-\sqrt5}{2+\sqrt5}=\frac{2-\sqrt5}{2+\sqrt5}*\frac{\sqrt5-2}{\sqrt5-2}=-\frac{4+5-4\sqrt5}{5-4}=4\sqrt5-9\\\\similarly,\ b=\frac{2+\sqrt5}{2-\sqrt5}=-(9+4\sqrt5)\\\\a^2-b^2=(a+b)(a-b)=-18*8\sqrt5=-144\sqrt5$