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

Hasan Naqvi
97 Points
6 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)(n- 5n + 22) = 0

I guess x + 1/x = 5

abhinav
13 Points
4 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
13 Points
4 years ago
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boom
13 Points
4 years ago
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boom
13 Points
4 years ago
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