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Question

If x+1x=3 then find x5+1x5.


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Solution

Solve for x5+1x5

It is given that x+1x=3

Squaring on both sides

x+1x2=9x2+1x2+2=9

x2+1x2=7…………..(1)

Similarly

x+1x3=27x3+1x3+3x21x+3x1x2=27x3+1x3+3x+31x=27x3+1x3+3x+1x=27x3+1x3+3×3=27x3+1x3=27-9

x3+1x3=18…………(2)

Multiply equation (1) and (2)

x2+1x2×x3+1x3=18×7x5+1x5+x+1x=126x5+1x5=126-3x5+1x5=123

Hence the value of x5+1x5is 123


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