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AFCAT Model Paper 3

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Question : 34 of 100

Marks: +1, -0

If

x^{2}+\frac{1}{x^{2}}=34

, then find the value of

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

0
1
2
3

Solution:

Given:

x^{2}+\frac{1}{x^{2}}=34

Formula Used:

●

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

●

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

Calculation:

We have

x^{2}+\frac{1}{x^{2}}=34

We know that,

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

⇒

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

⇒

\left(x+\frac{1}{x}\right)^{2}=34+2=36

[from equation (1)]

⇒

x+\frac{1}{x}=6

----(2)

Again, using the formula,

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

\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2}=x+\frac{1}{x}-2

⇒

\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2}=6-2=4

[From equation (2)]

\Rightarrow \sqrt{x} - \frac{1}{\sqrt{x}} = 2

∴ The value of $\sqrt{x} - \frac{1}{\sqrt{x}} \text{ is } 2.$

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