Question

(√6 + √5)^2 − (√6 − √5)^2

Answer 1

Answer:

$( \sqrt{6} + \sqrt{5} ) {}^{2} - ( \sqrt{6} - \sqrt{5} ) {}^{2} \\ let \: ( \sqrt{6} + \sqrt{5} ) = a \: and \: \\ ( \sqrt{6} - \sqrt{5} ) = b \\ (a {}^{2} - b {}^{2} ) = (a + b)(a - b) \\ ( \sqrt{6} + \sqrt{5} ) + ( \sqrt{6} - \sqrt{5} ) \\ \times ( \sqrt{6} + \sqrt{5} ) - ( \sqrt{6} - \sqrt{5} ) \\ = (\sqrt{6} + \sqrt{5} + \sqrt{6} - \sqrt{5} ) \\ \times ( \sqrt{6} + \sqrt{5} - \sqrt{6} + \sqrt{5} ) \\ = ( 2 \sqrt{6} )(2 \sqrt{5} ) = 4 \sqrt{30}$