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Alenka777
@Alenka777
July 2022
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Помогите решить уравнение :(
[tex] \sqrt[3]{x+7} + \sqrt[3]{9-x} =4 [/tex]
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m11m
(∛(x+7) + ∛(9-x))³ = 4³
x+7+9-x+3* ∛(x+7) * ∛(9-x) * (∛(x+7)+∛(9-x)) =64
16 + 3 * ∛[(x+7)(9-x)] * 4 =64
16+12 * ∛(9x+63-x²-7x)=64
4(4 + 3 * ∛(-x²+2x+63))=64
4+3 * ∛(-x²+2x+63)=16
3 * ∛(-x²+2x+63)=16-4
3 * ∛(-x²+2x+63)=12
∛(-x²+2x+63)=4
-x²+2x+63=4³
-x²+2x+63=64
-x²+2x+63-64=0
x²-2x+1=0
(x-1)² =0
x=1
Ответ: 1
2 votes
Thanks 1
Alenka777
Спасибо Вам огромное)))
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Answers & Comments
x+7+9-x+3* ∛(x+7) * ∛(9-x) * (∛(x+7)+∛(9-x)) =64
16 + 3 * ∛[(x+7)(9-x)] * 4 =64
16+12 * ∛(9x+63-x²-7x)=64
4(4 + 3 * ∛(-x²+2x+63))=64
4+3 * ∛(-x²+2x+63)=16
3 * ∛(-x²+2x+63)=16-4
3 * ∛(-x²+2x+63)=12
∛(-x²+2x+63)=4
-x²+2x+63=4³
-x²+2x+63=64
-x²+2x+63-64=0
x²-2x+1=0
(x-1)² =0
x=1
Ответ: 1