Question

simplify:
(2√2-5)²+(3√2+√3)²-(√2-1)²

Answer 1

HEYA!!

identity used:

$(x - y)^{2} = {x}^{2} - {y}^{2} + 2xy$

$(x + y)^{2} = {x}^{2} + {y}^{2} + 2xy$

on putting value in equation

$= ( {2 \sqrt{2} })^{2} + ( {5})^{2} - 20 \sqrt{2} +$

$({3 \sqrt{2} })^{2} + ( { \sqrt{3} })^{2} + 6 \sqrt{6} +$

$- ( { \sqrt{2} })^{2} + ( {1}^{2} ) - 2 \sqrt{2}$

$= 8 + 25 - 20 \sqrt{2} + 18 + 3 + 6 \sqrt{6}$

$- 2 - 1 + 2 \sqrt{2}$

$= 51 - 20 \sqrt{2} + 6 \sqrt{6} + 2 \sqrt{2}$

$= 51 - 18 \sqrt{2} + 6 \sqrt{6}$