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If x= 3+√2, find out value of √x+1/√x​

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Answer:

Step-by-step explanation:

BrainlyQueen01Maths AryaBhatta

Hey mate!

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GIVEN :

x = 2 + \sqrt{3}

To find :

x + \frac{1}{x}

Solution :

x = 2 + \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \TIMES \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{(2) {}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 - \sqrt{ 3}

Now,

x + \frac{1}{x} \\ \\ \IMPLIES 2 + \cancel{\sqrt{3}} + 2 - \cancel{ \sqrt{3}} \\ \\ \implies 2 + 2 \\ \\ \implies 4

Hence,

The answer is 4.

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Thanks for the question !


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