Question

Dacă x + 1/X = 5, atunci valoarea lui x² + 1/x² este: a)27 b)25 c)23 d)3​

Answer 1

$(x+\frac{1}{x} )^2=x^2+2x\frac{1}{x}+\frac{1}{x^2} \\ \Rightarrow 5^2=x^2+2+\frac{1}{x^2}\\ \Rightarrow x^2+\frac{1}{x^2}=25-2\\\Rightarrow x^2+\frac{1}{x^2}=23$

Answer 2

Explicație pas cu pas:

$x + \dfrac{1}{x} = 5$

$\Big(x + \dfrac{1}{x}\Big)^{2} = 5^{2}$

${x}^{2} + 2 \cdot x \cdot \dfrac{1}{x} + \dfrac{1}{ {x}^{2}} = 25$

${x}^{2} + \dfrac{1}{ {x}^{2}} = 25 - 2$

$\implies {x}^{2} + \dfrac{1}{ {x}^{2}} = 23$