Question

Arătați ca - 1 este soluție a ecuatiei 2x² + 3x(x-3) =-x² + 4(2-x) - 3x

Answer 1

2x²+3x(x-3)= -x²+4(2-x)-3x
2x²+3x²-9x= -x²+8-4x-3x
5x²+x² -9x+7x= 8
6x²-2x= 8
2(3x²-x)= 8
3x²-x= 4
x= -1⇒ 3(-1)²- (-1)= 4
 3·1+1=4
3+1=4
4=4 ⇒ Adevarat.

Answer 2

$2x^2+3x(x-3)=-x^2+4(2-x)-3x\\\\2x^2+3x\cdot x-3x\cdot3=-x^2+4\cdot2-4\cdot x-3x\\\\2x^2+3x^2-9x=-x^2+8-7x\\\\5x^2-9x=-x^2+8-7x\\\\5x^2+x^2=9x-7x+8\\\\6x^2=2x+8|\div2\\\\3x^2=x+4\\\\3x^2-x=4\\\\x(3x-1)=4$

[tex]Putem\ avea\ solutiile:\ 1.)\ x=-1\ ||\ 3x-1=-4\longrightarrow Convine\\\\ 2.)\ x=1\ ||\ 3x-1=4\longrightarrow Nu\ convine\\\\3.)\ x=2\ ||\ 3x-1=2\longrightarrow Nu\ convine\\\\4.)\ x=-2\ ||\ 3x-1=-2\longrightarrow Nu\ convine\\\\[/tex]

$Si\ inversele\ lor\,\ de\ asemenea\\\\ Deci,\ singura\ solutie\ adevarata\ este\ \boxed{\boxed{x=-1}}$