Question

Daca x+1/x=6, sa se calculeze x^2+1/x^2.
Doar 1/x si 1/x^2 sunt fractii, ^ insemnand ridicarea la putere.

Answer 1

$x+ \frac{1}{x}=6 \\ (x+ \frac{1}x})^2 =6^2 \\ x^{2} +2*x* \frac{1}{x}+ \frac{1}{ x^{2} } =36 \\ x^{2} + \frac{1}{ x^{2} } =36-2 \\ x^{2} + \frac{1}{ x^{2} } =34$

Answer 2

$\text{x}+\dfrac{1}{\text{x}} = 6\Big|^2 \Rightarrow \Big(\text{x}+\dfrac{1}{\text{x}}\Big)^2 = 6^2\Rightarrow \text{x}^2+2\cdot \not\text{x}\cdot \dfrac{1}{\not\text{x}}+\dfrac{1}{\text{x}^2} = 36 \Rightarrow \\ \\ \Rightarrow \text{x}^2+2+\dfrac{1}{\text{x}^2} = 36 \Rightarrow \text{x}^2+\dfrac{1}{\text{x}^2} = 36-2 \Rightarrow \boxed{\text{x}^2+\dfrac{1}{\text{x}^2} = 34}$