Question

Calculati x²+$\frac{1}{ x^{2} }$ ,stiind ca x-$\frac{1}{ x }$=4 (x$\neq 0$

Answer 1

( x + 1/x)²= 4² →

x² + 2x/x + 1²/x² = 16 →

x² + 2 + 1/x²= 16 →

x² + 1/x² = 14.

Answer 2

[tex]\it x-\dfrac{1}{x} =4\Leftrightarrow \left(x-\dfrac{1}{x}\right)^2 =4^2\Leftrightarrow x^2-2\cdot x\cdot\dfrac{1}{x} +\dfrac{1}{x^2} =16 \Leftrightarrow \\\;\\ \\\;\\ \Leftrightarrow x^2+\dfrac{1}{x^2} -2 =16 \Leftrightarrow x^2+\dfrac{1}{x^2} =16 +2 \Leftrightarrow x^2+\dfrac{1}{x^2} =18. [/tex]