On simplification the product of given expression x - 1x x - 1x x2 - 1x2 is -

The correct option is D x^4 1x^4 We need to find value of (x 1x) (x+1x) (x^2+1x^2) We know the identity #160; a^2 b^2 = (a b)(a+b) Then apply ...

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Standard VIII

Mathematics

Simplification of an Expression

On simplifica...

Question

On simplification the product of given expression $(x - \frac{1}{x}) (x + \frac{1}{x}) (x^{2} + \frac{1}{x^{2}})$ is ________.

x^{3} - \frac{1}{x^{3}}

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x^{3} + \frac{1}{x^{3}}

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

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

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Solution

The correct option is D $x^{4} - \frac{1}{x^{4}}$
We need to find value of $(x - \frac{1}{x}) (x + \frac{1}{x}) (x^{2} + \frac{1}{x^{2}})$
We know the identity $a^{2} - b^{2} = (a - b) (a + b)$
Then applying this to first two terms:
$(x^{2} - \frac{1}{x^{2}}) (x^{2} + \frac{1}{x^{2}})$
Again applying same identity:
$x^{4} - \frac{1}{x^{4}}$
Hence, option C is correct.

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Similar questions

If $x + \frac{1}{x} = 3$ , calculate $x^{2} + \frac{1}{x^{2}}, x^{3} + \frac{1}{x^{3}} a n d x^{4} + \frac{1}{x^{4}}$ .

If $x_{1}, x_{2}, x_{3}, x_{4}$ are four positive real numbers such that $x_{1} + \frac{1}{x_{2}} = 4, x_{2} + \frac{1}{x_{3}} = 1, x_{3} + \frac{1}{x_{4}} = 4$ and $x_{4} + \frac{1}{x_{1}} = 1,$ then

State true or false:

x \neq 0

and

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

, then:

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

$x^{5} + x^{4} + x^{3} + x^{2} + x + 1$ by $x^{3} + 1$

Q. x + 1 is a factor of the polynomial
(a) x³ + x²– x + 1
(b) x³ + x² + x + 1
(c) x⁴ + x³ + x² + 1
(d) x⁴ + 3x³ + 3x² + x + 1

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On simplification the product of given expression (x−1x)(x+1x)(x2+1x2) is ________.

The correct option is D x4−1x4We need to find value of (x−1x)(x+1x)(x2+1x2)We know the identity a2−b2=(a−b)(a+b)Then applying this to first two terms:(x2−1x2)(x2+1x2)Again applying same identity:x4−1x4Hence, option C is correct.

On simplification the product of given expression $(x - \frac{1}{x}) (x + \frac{1}{x}) (x^{2} + \frac{1}{x^{2}})$ is ________.