Question

DAU MULTE PUNCTE! Rezolvati va rog varianta 1 sau 2.

Answer 1

Varianta 1

1) 2^(4x+1) = 2^9

4x+1 = 9

4x = 8

x = 2

2) 4^(x²+5x+6) = 4^(2x)

x²+5x+6 = 2x

x²+3x+6 = 0

Delta = 9-24 = -15 < 0

Ecuatia nu are solutii in lR.

3) 2^(2x)*2^1 + 2^x * 2^2 = 160

Notam 2^x = t, t>0

2t²+4t-160 = 0|:2

t²+2t-80 = 0

Delta = 4-4*(-80) = 324

t1 = (-2+18)/2 = 8

t2 = -10 nu convine

=> 2^x = 8 => x=3

4) c.e. : 3x²-x-2 > 0

log2 (3x²-x-2) = log2 (8)

3x²-x-2 = 8

3x²-x-10 = 0

Delta = 1-4*3*(-10) = 121

x1 = (1+11)/6 = 2

x2 = (1-11)/6 = -10/6 = -5/3

Ambele solutii verifica c.e.

5) vezi poza

6) transform logaritmul in exponentiala

9^x - 6 = 3^x

3^(2x) - 3^x - 6 = 0

3^x = t, t>0

t²-t-6 = 0

Delta = 1-4*1*(-6) = 25

t1 = (1+5)/2 = 3

t2 = (1-5)/2 = -2 nu convine

=> 3^x = 3 => x=1

7) c.e. : x+2>0

√(x+2) = x | ( )²

-x²+x+2 = 0

Delta = 9

x1 = (-1+3)/(-2) = -1 nu convine

x2 = (-1-3)/(-2) = 2

8) √(x+1) = 5-x | ( )²

x²-11x+24 = 0

Delta = 25

x1 = 8 nu convine (prin inlocuire nu da acelasi rezultat in ambele parti)

x2 = 3

9) √(x²+5x+6) = √12 | ( )²

x²+5x+6 = 12

x²+5x-6 = 0

Delta = 49

x1 = (-5+7)/2 = 1

x2 = (-5-7)/2 = -6

Ambele sunt solutii.