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Grade: 9

                        

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

5 years ago

Answers : (5)

Hasan Naqvi
97 Points
							
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
Since the quadratic equation has no real answer, 
 
I guess x + 1/x = 5
 
5 years ago
abhinav
13 Points
							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.
						
3 years ago
boom
13 Points
							
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3 years ago
boom
13 Points
							
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3 years ago
boom
13 Points
							
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3 years ago
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