Question

Sa se rezolve ecuatia xpatrat +6x + radical din xpatrat + 6x = 20

Answer 1

x²+6x+√(x²+6x)=20
Notezi √(x²+6x) cu a si x²+6x va fi a²
a²+a=20
a²+a-20=0
Il descompui pe a in -4a+5a
a²-4a+5a-20=0
Dai factor comun
a(a-4)+5(a-4)=0
Dai factor comun din nou
(a-4)(a+5)=0
I.a-4=0⇒a=4
II.a+5=0⇒a=-5

I.
x²+6x=4²
x²+6x=16
x²+6x-16=0
Il descompui pe 6x in -2x+8x
x²-2x+8x-16=0
x(x-2)+8(x-2)=0
(x-2)(x+8)=0
I.x-2=0⇒x=2
II.x+8=0⇒x=-8

II.x²+6x=(-5)²
x²+6x=25
x²+6x-25=0
Δ=6²-4·1·(-25)=36+100=136
x1=(-6+√136)/2
x1=(-6+2√34)/2
x1=-3+√34
x2=(-6-√136)/2
x2=(-6-2√34)/2
x2=-3-√34

S={2, -8, -3+√34, -3-√34}