x-1x=3 then the value of x3-1x3 is?
Find the value of x3-1x3 using algebraic identities
Consider,
x-1x=3
Cubing both sides, we get
x-1x3=33=27
Now,
x-1x3=x3-1x3-3×x×1xx-1x∵a-b3=a3-b3-3aba-b⇒27=x3-1x3-3×1×3∵x-1x=3⇒27=x3-1x3-9⇒x3-1x3=27+9∴x3-1x3=36
Thus, the value of x3-1x3=36 .