Name: Application of (a²-b²)
Uploaded: 2019-07-19
Duration: 4 min 19 s
Description: Do you know what the application of (a^2 - b^2) in real life is? Have you ever even considered this question? Watch this video for complete information.

Question

If

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

, find the value of

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

and

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

Accepted Answer

Given that, $x + \frac{1}{x} = 2$

Taking square on both the sides.

$\Rightarrow {(x + \frac{1}{x})}^{2} = {(2)}^{2}$

We know that,

${(x + y)}^{2} = x^{2} + 2 x y + y^{2}$

Therefore,

$\Rightarrow {(x + \frac{1}{x})}^{2} = {(x)}^{2} + 2 (x) (\frac{1}{x}) + {(\frac{1}{x})}^{2} \Rightarrow {(2)}^{2} = x^{2} + 2 + \frac{1}{x^{2}} \Rightarrow 4 = x^{2} + 2 + \frac{1}{x^{2}} \Rightarrow x^{2} + \frac{1}{x^{2}} = 4 - 2 \Rightarrow x^{2} + \frac{1}{x^{2}} = 2 . . . . . (i)$

Now,

Squaring equation $(i)$ on both sides.

$\Rightarrow {(x^{2} + \frac{1}{x^{2}})}^{2} = {(2)}^{2} \Rightarrow {(x^{2})}^{2} + 2 (x^{2}) (\frac{1}{x^{2}}) + {(\frac{1}{x^{2}})}^{2} = 4 \Rightarrow x^{4} + 2 + \frac{1}{x^{4}} = 4 \Rightarrow x^{4} + \frac{1}{x^{4}} = 4 - 2 \Rightarrow x^{4} + \frac{1}{x^{4}} = 2$

Hence, the value of $x^{2} + \frac{1}{x^{2}}$ is $2$ and the value of $x^{4} + \frac{1}{x^{4}}$ is $2$ .

If $x + \frac{1}{x} = 2$ , find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{4} + \frac{1}{x^{4}}$

Important Questions on Identities

Learn and Prepare for any exam you want !

If x+1x=2, find the value of x2+1x2 and x4+1x4

Important Questions on Identities

Learn and Prepare for any exam you want !

If $x + \frac{1}{x} = 2$ , find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{4} + \frac{1}{x^{4}}$