Math, asked by ayushmang4428, 1 year ago

x - ( 1 )/( x ) = sqrt ( 3 );x ^ ( 3 ) - ( 1 )/( x ^ ( 3 ) )​

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Answers

Answered by Anonymous
3
(x-1/x)^3=x^3-1/x^3-3(x-1/x)
3(x-1/x)+(x-1/x)^2=x^3-1/^3
3root3+3=x^3-1/x^3
x^3-1/x^3=6root3
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ayushmang4428: answer is not clear
ayushmang4428: edit it and post it again
sivaprasath: Is my answer clear ?
ayushmang4428: yes
Answered by sivaprasath
5

Answer:

6√3

Step-by-step explanation:

Given :

If x - \frac{1}{x} = \sqrt{3} then,.

To find the value of : x^3 - \frac{1}{x^3}

Solution :

Given : x - \frac{1}{x} = \sqrt{3}

We know that,.

( a - b )² = a² - 2ab + b²

Substituting, a = x & b = \frac{1}{x}

We get,

(x - \frac{1}{x})^2 = (\sqrt{3})^2

x^ 2 - 2(x)(\frac{1}{x}) + (\frac{1}{x} )^2 = 3

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

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

x^2 + \frac{1}{x^2} = 5 ...(ii)

We also know that,

a³ - b³ = (a - b)(a² + ab + b²)

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

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

= (\sqrt{3})(5 + 1)= 6\sqrt{3}

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