Question

X^2 + 1 by x^2 = 83. find the value of x^3 - 1 by x^3

Answer 1

Answer:

x²+1/x²=83

subtracting 2 on both sides

x²-2+1/x²=83-2

(x-1/x)²=81

x-1/x=±9

Now,

x³-1/x³=(x-1/x)(x²+1/x²+x.1/x)

=9(x²+1/x²+1)

=9(83+1). {when taking x-1/x=9}

=9×84

=756

and x³-1/x³=(x-1/x)(x²+1/x²+1)

=-9(83+1)

=-9×84

=-756