Question

Rezolvati in R ecuati:modulul2x patrat-x-2=1,modulul x patrat+x-2=1-x,modulul -x patrat+5x-6=xpatra

Answer 1

|2x²-x-2| =1⇒ 2x²- x-2=1 sau 2x²- x-2= -1
2x²- x-2=1⇒ 2x²-x-3=0 ⇒ 2x²-3x+2x-3=0⇒ x(2x-3) +(2x-3)=0
⇒(2x-3)(x+1)=0⇒ x=3/2 sau x=-1
2x²- x-2= -1⇒ 2x²-x-1=0⇒ 2x²-2x+x-1=0⇒ 2x(x-1) + (x-1)=0
(x-1)(2x+1)=0⇒ x=1 sau x=-1/2

⇒ x∈{-1,1,3/2,-1/2}

|x²+x-2| =1-x
x²+x-2=1-x⇒ x²+2x-3=0⇒ x²+3x-x-3=0⇒ x(x+3) - (x+3)=0
(x+3)(x-1)=0⇒ x=-3 sau x=1
x²+x-2 = x-1⇒x²+x-x-2+1=0⇒ x²-1=0⇒ (x-1)(x+1)=0⇒ x=1 sau x=-1
x∈{-3,-1,1}

|-x²+5x-6|=x²
-x²+5x-6=x²⇒ -2x²+5x-6=0⇒2x²-5x+6=0⇒ x∈∅
-x²+5x-6= - x²⇒ 5x-6=0⇒ 5x=6⇒ x=6/5