Polynomials — Maths STD 9 — Question

$\Big(\text{x}^4+\frac{1}{\text{x}^4}\Big)=194$
$\Rightarrow(\text{x}^2)^2+\Big(\frac{1}{\text{x}^2}\Big)+2\times\text{x}^2\times\frac{1}{\text{x}^2}=194+2\times\text{x}^2\times\frac{1}{\text{x}^2}$
$\Rightarrow\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)^2=196$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}=\sqrt{196}=14$
Now,
$\Rightarrow(\text{x}^2)+\Big(\frac{1}{\text{x}^2}\Big)+2\times\text{x}\times\frac{1}{\text{x}}=14+2\times\text{x}\times\frac{1}{\text{x}}$
$\Rightarrow\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=16$
$\Rightarrow\text{x}+\frac{1}{\text{x}}=\sqrt{16}=4$
Now, $\Big(\text{x}+\frac{1}{\text{x}}\Big)^3=(4)^3$
$\Rightarrow(\text{x})^3+\Big(\frac{1}{\text{x}}\Big)^3+3\times\text{x}\times\frac{1}{\text{x}}\Big(\text{x}+\frac{1}{\text{x}}\Big)=64$
$\Rightarrow(\text{x}^3)+\Big(\frac{1}{\text{x}^3}\Big)+3(4)=64$
$\Rightarrow(\text{x}^3)+\Big(\frac{1}{\text{x}^3}\Big)=64-12 = 52$