Question

Ştiind că
$\sqrt{x} - \frac{1}{ \sqrt{x} } = 2$
, determinați
${x}^{2} + \frac{1}{ {x}^{2} }$
, unde x € (0, +∞).​

Answer 1

Răspuns:

34

Explica

√x-1/√x=2

Ridici    ecuatia  la  patrat

x+1/x-2√x/√x=4

x+1/x-2=4

x+1/x=6
Ridici     d in    nou    ecuatia   la    patrat
x²+1/x²+2x/x=36

x²+1/x²+2=36

x²+1/x²=36-2

x²+1/x²=34