Question

x^2+1/x^2=98
Find x^3+1/x^3=?

Answer 1

$x^{2} + \frac{1}{ x^{2} } =98 \\ \\ x^{2} + \frac{1}{ x^{2} } +2x( \frac{1}{x}) =98+2 \\ \\ (x+1/x)^{2} =100= 10^{2} \\ \\ x+1/x = 10$ 

x+1/x = 10 ----------(1)
And,
 (x+1/x)³ = 10³
  x³ + (1/x)³ + 3x.1/x(x+1/x) = 1000
  x³+ 1/x³ + 3(10)  = 1000    ..               (from eqn 1)
  x³ + 1/x³ =1000-30
  x³+ 1/x³ = 970

Answer 2

x² + 1/x² = 98
add 2 on both the sides and by doing that you will get
x² + 1/x² +2 = 100
or you can write it as
(x + 1/x )² =10²
⇒(x + 1/x ) = 10
cube on both sides
x³ +1/x³ =3x.1/x(x+1/x) = 1000
⇒we already know (x + 1/x ) = 10
so
x³ +1/x = 1000 - 30 = 970
so the answer in 970...