Question

x^4+1/x^4=47 show that x^3+1/x^3=18​

Answer 1

Answer:

x⁴+1/x⁴=47

or, x⁴+1/x⁴+2-2=47

or, {(x²)²+2.x².1/x²+(1/x²)²}=47+2

or, (x²+1/x²)²=49

or, (x²+1/x²)²=7²

or, x²+1/x²=7 [neglecting the negative sign]

or, x²+1/x²+2-2=7

or, x²+2.x².1/x²+1/x²=7+2

or, (x+1/x)²=9

or, (x+1/x)²=3²

or, x+1/x=3 [negnecting the negative sign]

∴, x³+1/x³

=(x+1/x)³-3.x.1/x(x+1/x)

=(3)³-3(3)

=27-9

=18 .