Question

1.determinati a∈R astfel incat -2 sa fie solutie a ecuatiilor cu necunoscuta x∈ R :

a) 3x+a=2x-12
b)5x+a=3x+2

2. rezolvati in R ecuatiile:
a) (x-2)(3x-√2)=0
b) |x-2|=4
c) 2x-√2 =√8
d)√2x -4=2x-2√2

Answer 1

1.
a)3(-2)+a=2(-2)-12
-6+a=-14
a=-8
b)5(-2)+a=3(-2)+2
-10+a=-6+2
a=10-4
a=6

2.
a)3x²-√2x-6x+2√2=0
   3x²-x(√2+6)+2√2=0
Δ=(√2+6)²-4·3·2√2
Δ=2+12√2+36-24√2
Δ=38-12√2

b)x-2=4 =>x=6
   -x+2=4 =>x=-2

c)2x=2√2+√2
   2x=3√2  =>x=3√2/2

d)√2x-2x=4-2√2
x(√2-2)=2(2-√2) =>x=2(2-√2)/(√2-2)=-2(√2-2)/(√2-2) =>x=-2