Question

give me the whole solution

Answer 1

Given Equation is x^2 + 1/x^2 = 79

We know that (x + 1/x)^2 = x^2 + 1/x^2 + 2

                                        = 79 + 2

                                        = 81

                         (x + 1/x) = 9.


Now,

We know that (x + 1/x)^3 = x^3 + 1/x^3 + 3(x + 1/x)

                         (9)^3 = x^3 + 1/x^3 + 3(9)

                         729 = x^3 + 1/x^3 + 27

                         x^3 + 1/x^3 = 702.


Hope this helps!

Answer 2

Hi friend
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Your answer
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Given that : - x² + 1/x² = 79

To calculate : - Value of x³ + 1/x³.

Now,
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x² + 1/x² = 79

=> x² + 1/x² + 2 = 79 + 2 [Adding 2 on both sides.]

=> (x + 1/x)² = 81

=> x + 1/x = √81

=> x + 1/x = 9 ......(i)

Then,
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x³ + 1/x³

= (x + 1/x)(x² - x . 1/x + 1/x²)

=> 9 × {(x² + 1/x²) - 1} [From (i)]

=> 9 × (79 - 1)

=> 9 × 78

=> 702

Therefore,
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x³ + 1/x³ = 702

HOPE IT HELPS