I f X+1/X=3 the value of X^5+1/X^5is

RRB NTPC Mains or Stage 2 Model Paper 3 with solutions

Question : 20 of 120

Marks: +1, -0

I f

X+1/X=3

the value of

X^5+1/X^5

Solution:

X+1/X=3

by squaring

X^2+1/X^2+2=9

X^2+1/X^2=7

... (2)
Taking cube on both side, to equation (1)

[X+1/X]^3=27

X^3+1/X^3+3[X+1/X]=27

From equation (2) and (3)

[X^2+1/X^2][X^3+1/X^3]=18×7

X^5+1/X^5+X+1/X=126

X^5+1/X^5=126-3=123

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