Question

imi puteti rezolva ecuatia x2 - 4x = 6

Answer 1

x²-4x=6 (mutam 6 in partea stanga cu semn schimbat)
x²-4x-6=0

avem o ecuatie de gradul II
a=1
b=-4
c=-6

calculam Δ(delta)
Δ=b²-4ac
 =(-4)²- 4·1·(-6)
 =16-(-24)
 =16+24
 =40

Δ>0 ⇒ ecuatia are 2 solutii reale distincte

$x_{1} = \frac{-b+ \sqrt{delta} }{2a}= \frac{-(-4)+ \sqrt{40} }{2*1}= \frac{2*2+2 \sqrt{10} }{2} = \frac{2*(2+ \sqrt{10}) }{2}= 2+ \sqrt{10}$

$x_2 = \frac{-b- \sqrt{delta} }{2a} = \frac{-(-4)- \sqrt{40} }{2*1} = \frac{2*2-2 \sqrt{10} }{2} =\frac{2*(2- \sqrt{10)} }{2}=2-\sqrt{10}$

S={2+√10 ; 2-√10}