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kodGreya [7K]
4 years ago
10

Find the value of x given that

Mathematics
1 answer:
Elodia [21]4 years ago
7 0

For the first part, the results get quite crazy. I hardly believe that you're supposed to do this by hand, so I'm afraid that there's some typo in the question.

As for the second part, we have

\sqrt{x}+\dfrac{1}{\sqrt{x}}=\dfrac{x+1}{\sqrt{x}}

Plug your value for x and you have

\dfrac{x+1}{\sqrt{x}} \mapsto \dfrac{4+2\sqrt{2}}{\sqrt{3+2\sqrt{2}}}=\dfrac{4+2\sqrt{2}}{1+\sqrt{2}}

We can rewrite the quantity as

\dfrac{4+2\sqrt{2}}{1+\sqrt{2}}\cdot\dfrac{1-\sqrt{2}}{1-\sqrt{2}}=\dfrac{4-4\sqrt{2}+2\sqrt{2}-4}{-1} = 2\sqrt{2}

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Step-by-step explanation:

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