Question

НАЙТИ X ИЗ ПРОПОРЦИИ!
НЕСЛОЖНО

Answer 1

$\frac{a ^{2} +b ^{2} +2ab}{a ^{2} -b ^{2} } = \frac{x}{a ^{2} -2b ^{2} +ab} \\ \\ \frac{a ^{2} +b ^{2} +2ab}{a ^{2} -b ^{2} }= \frac{(a+b) ^{2} }{(a-b)(a+b)}= \frac{a+b}{a-b} \\ \\ \frac{a+b}{a-b} = \frac{x}{a ^{2} -2b ^{2} +ab}$

$x= \frac{(a+b)(a ^{2} -2b ^{2} +ab)}{a-b} = \frac{a ^{3} -2ab^{2}+a ^{2} b+a ^{2} b+2b ^{3}+ab ^{2} }{a-b} = \frac{a ^{3} +2a ^{2} b-ab ^{2}-2b ^{3} }{a-b} = \\ = \frac{a ^{2} (a+2b)-b^{2}(a+2b) }{a-b} = \frac{(a ^{2} -b ^{2} )(a+2b)}{a-b} = \frac{(a-b)(a+b)(a+2b)}{a-b} = \\ = (a+b)(a+2b)=a ^{2} +2ab+ab+2b ^{2} =a ^{2} +3ab+2b ^{2}$