Tuesday 20 December 2011

Algebra-29

If (x2+1)/x = 5, then find the value of (x12+1)/x6?
(1)120098      (2) 5    (3) 12100       (4) 56   (5) none of these
Solution follows here:
Solution:
This is a bit changed in shape from the traditional one,
“If x + 1/x = 5 then find x6 + 1/x6
As we need to find 6th power, first we proceed for cube
x + 1/x = 5 => (x + 1/x)3 = 53
Formula to be used here : (a+b)3 = a3+b3+3ab(a+b)
=> x3 + 1/x3 + 3x(1/x)(x+1/x) = 125
=> x3 + 1/x3 + 3 (5) = 125
=> x3 + 1/x3 = 110
Now squaring on both sides,
(x3 + 1/x3)2  = 1102
Formula to be used here : (a+b)2 = a2+b2+2ab
=> x6 + 1/x6 + 2x3(1/x3) = 12100
=> x6 + 1/x6 + 2 = 12100
=> x6 + 1/x6 = 12098
Be careful at the answer options, 120098 is given to trap.
Answer (5)

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