Grade 99 grade maths

If xcube + 1/xcube = 110, then x+1/x = ?

Sidharth Mathur

11 Years agoGrade 9

5 Answers

Hasan Naqvi

11 Years ago

let x + 1/x =n

then

(x + 1/x) ³ =n³

= x³ + 1/x³ + 3 * x * 1/x² + 3 * x² * 1/x

=110 + 3/x + 3x

=110 + 3(x + 1/x )

=110 + 3n

Now solving,

n³= 110 +3n

n³ – 3n -110 = 0

Putting n =5(one of the factors of 110), we this eqn to reduce to 0

So dividing this equation by n-5

(n-5)(n²- 5n + 22) = 0

Since the quadratic equation has no real answer,

I guess x + 1/x = 5

abhinav

9 Years ago

Let x+1/x be y - [1]Then (x+1/x)³=x³+1/x³+3(x+1/x)y³=110+3y [from 1and x³+1/x³=110]y³ here is a perfect cube as we know y. Therefore we must find a number whose whose cube is near 110 and greater than 110 by 3 times of it. So the cube of 5 is is very near to 110 which is 125 and on subtracting 110 we get 15 which can be written as 3 x 5. So y equal to 5. So 5 is the required answer.

boom

9 Years ago

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boom

9 Years ago

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