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if x be the real number such that x 3 +4x=8,then value of the expression x 7 +64x 2 is......

if x be the real number such that x3+4x=8,then value of the expression x7+64x2 is......

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
For any integer n\geq 0,the given equation impliesxn+3=-4xn+1+8xn
so we can write such power of x in terms of lower powers.
carrying out this process iteratively gives
x7=-4x5+8x4
=8x4+16x3-32x2
=16x3-64x2+64x
=-64x2+128
so x7+64x2=128
Hence the answer is 128

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