Question

Rezolvati ecuatia (x²-2)*3=2


* =compus

Answer 1

Răspuns:

$\bf{x = \pm \frac{2 \sqrt{6} }{3} }$

Explicație pas cu pas:

$\mathbf{(x {}^{2} - 2) \times 3 = 2}$

$\mathbf{ {3x}^{2} - 2 \times 3 = 2 }$

$\mathbf{3x {}^{2} - 6 = 2 \Longleftrightarrow3x {}^{2} = 2 + 6 = 8 }$

$\mathbf{x {}^{2} = \frac{8}{3} \: \Longrightarrow \: x =\pm \sqrt{ \frac{8}{3} } = \pm \frac{2 \sqrt{6} }{3} }$

$\boxed{ \bf{ S = \left\{ - \frac{2 \sqrt{6} }{3} ; \: \frac{2 \sqrt{6} }{3} \right\}}}$

Succes ! :)

Answer 2

Răspuns:

Explicație pas cu pas:

x*y=xy+x+y-1 = legea de compozitie .

(x²-2)*3=2, ⇒ (x²-2)·3+x²-2+3-1=2, ⇒4·(x²-2)+2=2, ⇒4·(x²-2)=0, ⇒ x²-2=0, ⇒ x²=2, ⇒ x=±√2.

Răspuns: S={-√2:  √2}