Question

Clasa a9-a mate , am nevoie de ajutor :( . Exercițiu 1

Answer 1

a)
x²-11x+18=0
Δ=(-11)²-4×18×1=121-72=49
x₁=(11+√49)/2=(11+7)/2=9
x₂=(11-√49)/2=(11-7)/2=2

b)(x-3)/(x²-5x+6)=2
x-3=2x²-10x+12
2x²-11x+15=0
Δ=(-11)²-4×15×2=121-120=1
x₁=(11+√1)/4=(11+1)/2=3
x₂=(11-√1)/2=(11-1)/4=5/2

c)-x²+5x-6≥0
-x²+5x-6=0 
Δ=(5)²-4×(-1)×(-6)=25-24=1
x₁=(-5+√1)/2×(-1)=-4/(-2)=2
x₂=(-5-√1)/2×(-1)=-6/(-2)=3

x                                        x₁                              x₂
                                          2                              3
-x²+5x-6             -  -          0          + + +            0   - - -
x∈[2,3]

d)3x-6≤4(1-x)+2
3x-6≤4-4x+2
7x-12≤0
7x≤12
x≤12/7

x                                12/7
7x-12        - - - -           0         ++++
x∈(-∞ , 12/7]