Question

find the value of x^3+1/x^3 if x^2+1/x^2=14​

Answer 1

x²+1/x²=14

=>x²+1/x²=16-2

=>x²+1/x²+2=16

=>x²+1/x²+2(x)(1/x)=16. [since 1=(x)(1/x)]

=>(x+1/x)²=16

=>x+(1/x)=√16

=>x+(1/x) =4

we know that a³+b³=(a+b)(a²-ab+b²)

there fore

x³+(1/x³)=(x+1/x)(x²-1+1/x²)

=>x³+1/x³=(4)(14-1) [since x²+1/x²=14]

=>x³+1/x³=(4)(13)

=>x³+1/x³=52

HOPE YOU UNDERSTAND THE ANSWER