Question

if (x+1/x) = 4,
find the value of
(i) (x-1/x)
(ii) (x^3 - x^3)​

Answer 1

Step-by-step explanation:

1) square on both sides

(x+1/x)^2=16

x^2 +1/x^2+2*x*(1/x)=16

x^2+1/x^2+2=16

x^2+1/x^2=16-2=14

x^2+1/x^2=14

take out 2 from both sides

x^2+1/x^2-2= 14-2

(x-1/x)^2 =12

x-1/x =√12

11)

(x^3-1/x^3)=(x-1/x)(x^2+x*(1/x)+1/(x^2))

= (√12)*(14+1)

=15*√12

=15*2√3

=30√3