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AFCAT Model Paper 4

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Question : 68 of 100

Marks: +1, -0

If

2 x^{2} + \frac{1}{3 x^{2}} = 6

, then find the value of

9 x^{4} + \frac{1}{4 x^{4}}

214
38
88
78

Solution:

Given:

2 x^{2} + \frac{1}{3 x^{2}} = 6

Formula used:

(a+b)^{2}=a^{2}+b^{2}+2 a b

As,

2 x^{2} + \frac{1}{3 x^{2}} = 6

Multiplying both sides by

\left( \frac{3}{2} \right) \times \left( 2 x^{2} + \frac{1}{3 x^{2}} \right) = 6 \times \frac{3}{2}

, we’ll get

⇒

3 x^{2} + \frac{1}{2 x^{2}} = 9

Now squaring both sides, we’ll get

\left( 3 x^{2} + \frac{1}{2 x^{2}} \right)^{2} = 9^{2}

⇒

9 x^{4} + \frac{1}{4 x^{4}} + 2 \times 3 x^{2} \times \frac{1}{2 x^{2}} = 81

⇒

9 x^{4} + \frac{1}{4 x^{4}} + 3 = 81

⇒

9 x^{4} + \frac{1}{4 x^{4}} = 81 - 3

∴ $9 x^{4} + \frac{1}{4 x^{4}}$ is 78

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