Question

This is A math problem.​

Answer 1

ANSWER.

• The value of (x + 1/x) is 2√2.

SOLUTION.

Given –

$\tt \implies x = \dfrac{1}{ \sqrt{2} + 1 }$

• We have to find out the value of (x + 1/x)

From here, we get,

$\tt \implies \dfrac{1}{x} = \sqrt{2} + 1$

Rationalising x, we get,

$\tt \implies x = \dfrac{1}{ \sqrt{2} + 1 } \times \dfrac{ \sqrt{2} - 1}{ \sqrt{2} - 1}$

$\tt \implies x = \dfrac{ \sqrt{2} - 1 }{( \sqrt{2} + 1 )( \sqrt{2} - 1)}$

Using identity a² - b² = (a + b)(a - b), we get,

$\tt \implies x = \dfrac{ \sqrt{2} - 1 }{2 - 1}$

$\tt \implies x = \sqrt{2} - 1$

Therefore,

$\tt \implies x + \dfrac{1}{x} = \sqrt{2} - 1 + \sqrt{2} + 1$

$\tt \implies x + \dfrac{1}{x} = 2\sqrt{2}$

★ So, the value of (x + 1/x) is 2√2.

Answer 2

Answer:

the answer is 2√2

Step-by-step explanation:

x=1/√2+1

x+1/x

=(2x+1)/x

=[(2 * 1/√2+1 )+1]/1/√2+1

here you cancel and get 2√2

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