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Telangana TET Paper 2 Math and Science Model Paper 2

Section: Math and Science

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Question : 138 of 150

Marks: +1, -0

If x = 5 +

2\sqrt{6}

\frac{(x-1)}{\sqrt{x}}

is equal to

$\sqrt{2}$
$2\sqrt{2}$
$\sqrt{3}$
$2\sqrt{3}$

Solution:

Concept:

Express

x

as a perfect square using the identity

(√a+√b)^2 = a+b+2√{ab}

.

Explanation:

Given

x = 5+2√6

. Write

5

as

2+3

and

2√6

as

2√{2×3}

.

So

x = (√2)^2+(√3)^2+2×√2×√3 = (√2+√3)^2

.

Then

\frac{x-1}{√x} = \frac{5+2√6-1}{√{(√2+√3)^2}} = \frac{4+2√6}{√2+√3}

.

Factor numerator:

4+2√6 = 2√2(√2+√3)

.

Cancel the common factor:

\frac{2√2(√2+√3)}{√2+√3} = 2√2

.

Answer:

Option B.

2√2

.

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