Latest Others Aptitude Question SOLUTION: if (x^2+1)/x=5 then find the value of (x^12+1)/x^6

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if (x^2+1)/x=5 then find the value of (x^12+1)/x^6

Asked In Others prashanthi (11 years ago)

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phani  (11 years ago)

12098

(x^2+1)/x=5
==>x+1/x=5
==>x^2+1/x^2=23(squaring on both sides)
==>x^4+1/x^4=527(square on both sides)........(1)
(1)*x^2=>x^6+1/x^2=527x^2.........(2)

(1)/x^2=>x^2+1/x^6=527/x^2.....(3)
(1)+(2)==>
X^6+1/X^6+(x^2+1/x^2)=527(x^2+1/x^2)
==>x^6+1/x^6=526*23
==>(x^12+1)/x^6=12098

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Aman  (11 years ago)

12098

(x^2+1)/x=5
x+1/x = 5
x^2+1/x^2 = 5^2-2= 23
cubing both sides,
x^6+ 1/x^6 +3*x^2*(1/x^2) *(x^2+1/x^2) = 23^3
x^6+1/x^6 = 23^3 -3*1*23 = 12167-69
x^6+1/x^6 = 12098 = (x^12+1)/x^6

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chaitanya  (11 years ago)

5
as x^2/x so
x^12/x^6=5

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