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What are the solutions to this equation?

1
-1
√17
-√17
There are no solutions.

What are the solutions to this equation? 1 -1 √17 -√17 There are no solutions.-example-1

2 Answers

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5-\sqrt[3]{x^2-9}=7\implies 5=\sqrt[3]{x^2-9}+7\implies -2=\sqrt[3]{x^2-9} \\\\\\ (-2)^3=(\sqrt[3]{x^2-9})^3\implies -8=x^2-9\implies 1=x^2 \\\\\\ \pm√(1)=x\implies \pm 1 = x

User Vo Kim Nguyen
by
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4 votes

Answer:

1 and -1

Explanation:


5 - \sqrt[3]{( {x}^(2) - 9 } = 7


- \sqrt[3]{( {x}^(2) - 9} = 7 - 5


- \sqrt[3]{( {x}^(2) - 9} = 2


\sqrt[3]{( {x}^(2) - 9} = - 2

Cube both sides of the equation:


{x}^(2) - 9 = { - 2}^(3)


{x}^(2) - 9 = - 8


{x}^(2) = - 8 + 9


{x}^(2) = 1


{x}^(2) - 1 = 0


(x - 1)(x + 1) = 0


x = 1 \: \: or \: \: x = - 1

User Tehras
by
7.7k points

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