Question

if x+1/x=7,find value of x^3-1/x^3​

Answer 1

if; x+ 1/x=7

if; x+ 1/x=7then, (x+1/x)^2=7^2=49

if; x+ 1/x=7then, (x+1/x)^2=7^2=49or, (x+1/x)^2-4. x.1/x=49-4

if; x+ 1/x=7then, (x+1/x)^2=7^2=49or, (x+1/x)^2-4. x.1/x=49-4or, (x-1/x)^2=44

if; x+ 1/x=7then, (x+1/x)^2=7^2=49or, (x+1/x)^2-4. x.1/x=49-4or, (x-1/x)^2=44or, x-1/x=44^1/2

Now,,,,

x^3-1/x^3

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

=(44^1/2){(x-1/x)^2+2x.1/x-x.1/x}

=(44^1/2) (44+1)

=45.44^1/2