Question

if (x^2) +(1/x^2)=66 find the value of( x^3)-(1/x^3)

Answer 1

x^2 + 1/x^2=66

=) (x- 1/x)^2 + 2(x^2×1/x^2) =66

=) (x- 1/x)^2 +2 = 66

=) (x- 1/x)^2 =66-2=64

=) (x- 1/x)^2 = 64

=) x- 1/x =8
$\sqrt{64} = 8$
☆ (x^3 - 1/x^3)
we can write the formula here
a^3 -b^3 =(a-b)^3 + 3ab(a-b)

= (x- 1/x)^3 + 3 x × 1/x (x- 1/x)

= ( 8 )^3 +3×8

=512+24

=536