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If X 3 + 1 X 3 = 110 , Then X + 1 X = - Mathematics

MCQ

If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]

Options

  • 5

  • 10

  • 15

  • none of these

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Solution

In the given problem, we have to find the value of  `x + 1/x`

Given  `x^3 + 1/x^3 = 110`

We shall use the identity `(a + b)^3 = a^3 + b^3 + 3ab (a+b)`

`(x+1/x)^3 = x^3 + 1/x^3 + 3 xx x xx 1/x(x+ 1/x)`

`(x+1/x)^3 = x^3 + 1/x^3 + 3 (x+ 1/x)`

Put  `x + 1/x = y`we get,

 `(y)^3 = x^3 + 1/x^3 + 3 (y)`

Substitute y = 5 in the above equation we get

                 `(5)^3 = x^3 + 1/x^3 + 3(5)`

                   `125 = x^3 + 1/x^3 + 15`

          `125 - 15 = x^3 + 1/x^3`

                    `110 = x^3 + 1/x^3`

The Equation `(y)^3 = x^3 + 1/x^3 + 3(y)` satisfy the condition that  `x^3 + 1/x^3 = 110`

Hence the value of  `x+ 1/x` is 5.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 4 Algebraic Identities
Q 6 | Page 30
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