If (x

^{2}+1)/x = 5, then find the value of (x^{12}+1)/x^{6}?
(1)120098 (2) 5 (3) 12100 (4)
5

Solution
follows here:^{6}(5) none of these__Solution:__
This is a bit changed in shape from the traditional one,

“If x + 1/x = 5 then find x

^{6}+ 1/x^{6 }“
As we need to find 6th power, first we proceed for cube

x + 1/x = 5 => (x + 1/x)

Formula to be used here : (a+b)

^{3}= 5^{3}Formula to be used here : (a+b)

^{3}= a^{3}+b^{3}+3ab(a+b)
=> x

^{3}+ 1/x^{3}+ 3x(1/x)(x+1/x) = 125
=> x

^{3}+ 1/x^{3}+ 3 (5) = 125
=> x

^{3}+ 1/x^{3}= 110
Now squaring on both sides,

(x

(x

^{3}+ 1/x^{3})^{2}= 110^{2}
Formula to be used here : (a+b)

=> x

^{2}= a^{2}+b^{2}+2ab=> x

^{6}+ 1/x^{6}+ 2x^{3}(1/x^{3}) = 12100
=> x

^{6}+ 1/x^{6}+ 2 = 12100
=> x

Be careful at the answer options, 120098 is given to trap.

Answer (5)^{6}+ 1/x^{6}= 12098Be careful at the answer options, 120098 is given to trap.

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