Question

решите уровнение
(x+y)³ (x-y)²=27
(x-y)³ (x+y)²=9
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Answer 1

Ответ:

Объяснение:

$\left \{ {{(x+y)^{3} (x-y)^{2} =27} \atop {(x-y)^{3} (x+y)^{2} =9}} \right.$ ⇔ $\left \{ {{x = 2y} \atop {(2y-y)^{3}(2y+y)^{2} =9 }} \right.$  ⇔ $\left \{ {{x=2y} \atop {y=1}} \right.$ ⇔ $\left \{ {{x=2*1} \atop {y=1}} \right.$  ⇔$\left \{ {{x=2} \atop {y=1}} \right.$

1) Поделим уравнения друг на друга:

$\frac{(x+y)^{3} (x-y)^{2} }{(x-y)^{3} (x+y)^{2}}$  = $\frac{27}{9}$

$\frac{x+y}{x-y}$ = 3

3(x-y)=x+y

3x-3y=x+y

3x-x-3y-y=0

2x-4y=0  / 2

x-2y = 0

x = 2y

2)Решим (2y-y)³(2y+y)² = 9

y³ * (3y)² = 9

y³ * 9y² = 9  /9

y³ * y² = 1

$y^{5}$ = 1

y=1