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UPTET Paper 2 Math and Science Model Test 4

Section: Mathematics and Science

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Question : 131 of 150

Marks: +1, -0

If

x+\frac{16}{x}=8,

then the value of

x^{2}+\frac{32}{x^{2}}

is:

24
18
20
16

Solution:

Concept:

If

x + \frac{a}{x} = 2\sqrt{a}

, then

x = \sqrt{a}

. This pattern helps find

x

directly without solving the quadratic.

Explanation:

Given:

x + \frac{16}{x} = 8

.

Notice that

2\sqrt{16} = 2 \times 4 = 8

. So the equation matches the pattern with

a = 16

.

Thus,

x = \sqrt{16} = 4

.

Now compute the required expression:

x^{2} + \frac{32}{x^{2}}

.

Substitute

x = 4

:

4^2 + \frac{32}{4^2} = 16 + \frac{32}{16} = 16 + 2 = 18

.

Hence, the value is 18.

Answer:

The value is 18, which corresponds to option B.

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