Question

If x = 5+2√6 find the value of √x+1/√x

Answer 1

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$x = 5 + 2 \sqrt{6} \\ \\ ⇒ \frac{1}{x} = \frac{1}{5 + 2 \sqrt{6} } \times \frac{5 - 2 \sqrt{6} }{5 - 2 \sqrt{6} } \\ \\ ⇒ \frac{1}{x } = \frac{5 - 2 \sqrt{6} }{25 - 24} = 5 - 2 \sqrt{6}$

Now,

⇒x = 5 + 2√6

⇒x = 3 + 2 + 2√3√2

⇒x = (√3)² + 2√3√2 + (√2)²

⇒x = (√3 + √2)²

⇒√x = √3 + √2

Now,

⇒1/√x = 1/√3 + √2

⇒1/√x = 1/√3 + √2 × √3 - √2/√3 - √2

⇒1/√x = √3 - √2/3 - 2

⇒1/√x = √3 - √2

$\therefore$ √x + 1/√x

⇒√3 + √2 + √3 - √2

⇒√3 + √3

⇒2√3

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Answer 2

Answer:

here is ur ans....

x=5+2

6

⇒

x

1

=

5+2

6

1

×

5−2

6

5−2

6

⇒

x

1

=

25−24

5−2

6

=5−2

6

Now,

x = 5 + 2√6

x = 3 + 2 + 2√3√2

x = (√3)² + 2√3√2 + (√2)²

x = (√3 + √2)²

√x = √3 + √2

Now,

1/√x = 1/√3 + √2

1/√x = 1/√3 + √2 × √3 - √2/√3 - √2

1/√x = √3 - √2/3 - 2

1/√x = √3 - √2

∴\therefore∴ √x + 1/√x

√3 + √2 + √3 - √2

√3 + √3

2√3 ... ans

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