Question

Sa se compuna o ecuatie cu gradul 2 a urmatoarelor solutii.

Answer 1

a)x₁+x₂=S si x₁x₂=P
x²-Sx+P=0 =>in cazul nostru x²-8x+15=0
Verif. Δ=(-8)²-4·15; Δ=64-60; Δ=4 =>√Δ=2
x₁=(8-2)/2=3 si x₂=(8+2)/2=5
b)S=-1 si P=-6 =>x²+x-6=0
Verif. Δ=1-4(-6); Δ=1+24; Δ=25 =>√Δ=5
x₁=(-1-5)/2=-3 si x₂=(-1+5)/2=2
c)S=0 si P=-5 =>x²-5=0
d)3x+3-10x-12=7
-7x-9-7=0
-7x-16=0
-7x=16 sau 7x=-16 =>x=-16/7
e)7x+28-8x+1≥7
-x+29-7≥0
-x+22≥0
-x≥-22 sau x≤22
f)4x+6x-10<0
10x<10 =>x<1
g)8x²-4x+4>0 l:4
2x²-x+1>0
Δ=1-8=-7 =>inecuatia nu are solutii reale
h)3x²-9x≥0
Δ=(-9)²=81 =>√Δ=9
x₁=(9-9)/6=0 si x₂=(9+9)/6=3
i)x/2 + 4 -15x - 35 ≥ 0 l·2
x-30x-62≥0
-29x≥62 sau 29x≤-62 =>x≤-62/29

3x+3-10x-12=7
-7x-9-7=0
-7x-16=0
-7x=16 sau 7x=-16 =>x=-16/7