Question

Rezolvati in multimea nr. reale ecuatiile:
a) 2|x-2|+7=3|x-2|
b) 5(x+1)²-3(3x-4)=(2x-1)²+(x-2)(x+2)
Aflati solutiile reale ale ecuatiei:
3(x-9)+5|x-9|=4(x-5)

Answer 1

2|x-2|+7=3|x-2|
|x−2|=7 => x−2=7, deci x=9 și x−2=−7, deci x=-5

5(x+1)²-3(3x-4)=(2x-1)²+(x-2)(x+2)
5x^2+x+17=5x^2−4x−3
5x=−20
x= -4

3(x-9)+5|x-9|=4(x-5)
5(|x−9|)+3x−27=4x−20

5(|x−9|)=x+7
|x−9|=(x+7)/5

x−9= x/5+7/5
4x=52
x=13

x-9= -x/5-7/5
6x=38
x=19/3