Question

Fie a=(3x-2)(x+1)-3(x-1)*2 ,x€R.Rezolvati in multimea numerelor reale ecuatiile:
a)a=2
b)a*2=81
c)|a|=1
d)a-16=0

Answer 1

a = (3x - 2)(x + 1) - 3(x - 1)²= (3x² + 3x -2x -2) -3 (x²-2x+1) = (3x² + x - 2) - 3x² + 6x -3 = 7x - 5 deci a = 7x - 5

a)

a = 2

2 = 7x - 5

2 + 5 = 7x

7 = 7x

x = 1

b)a² =81 dar a = 7x - 5

(7x -5 )² = 81

7x - 5 = 9

7x =9 +5

7x = 14

x = 2

c)

IaI = 1 dar a = 7x - 5

I7x - 5 I =1

IxI ={x, x≥0} si IxI ={-x, x<0}

deci

1. I7x - 5 I =1 pentru x≥0, ⇒ 7x - 5 = 1⇒ 7x = 1 + 5⇒x = 6/7

2.1. I7x - 5 I =1 pentru x<0, ⇒ 7x - 5 = - 1⇒ 7x = - 1 + 5⇒x = 4/7

S = { 6/7 ; 4/7 }

d)

a -16 = 0 dar a = 7x - 5

7x - 5 -16 = 0

7x = 21

x = 3