Question

stiind ca:
$x + \frac{1}{x} = \sqrt{11}$
x€R*, atunci suma
${x}^{2} + \frac{1}{ {x}^{2} } \: este \: egala \: cu$
a) 9
$b) \: 2 \sqrt{11}$
$c) \: 3 \sqrt{11}$
d) 4
​

Answer 1

x+1/x=√11 |²

(a+b)²=a²+2ab+ b²

x² + 2×x×(1/x) + 1/x² =11

x² +2 +1/x²=11

x² + 1/x² =9