Question

Folosind teorema lui Viete,rezolvati an R ecuatia:
a)x2-3x-180=0
b)x2+5x-150=0

Answer 1

x²-3x-180=0

x₁+x₂=3, x₁x₂=-180
x₁=15, x₂=-12

x₂+5x-150=0
x₁+x₂=-5, x₁x₂=-150,
x₁=10, x₂=-15

Answer 2

a)x²-3x-180=0
a=1
b=-3
c=-180
Δ=(-3)²-4×1×(-180)=9+720=729
x₁=(3+√729)/2=(3+27)/2=15
x₂=(3-√729)/2=(3-27)/2=-12
relatiile lui viete
x₁+x₂=-b/a=-(-3)/1=3
x₁ × x₂=c/a=(-180)/1=-180
x₂=3-x₁
x₁(3-x₁)=-180
3x₁-x₁²=-180
x₁²-15x₁+12x₁-180=0
x₁(x₁-15)+12(x₁-15)=0
(x₁-15)(x₁+12)=0
x₁-15=0  x₁=15
x₁+12=0  x₁=-12



 b)x²+5x-150=0
a=1
b=5
c=-150
Δ=5²-4×1×(-150)=25+600=625
x₁=(-5+√625)/2=(-5+25)/2=10
x₂=(-5-√625)/2=(-5-25)/2=-15

relatiile lui viete
x₁+x₂=-b/a=-(5)/1=-5
x₁ × x₂=c/a=(-150)/1=-150
x₂=-x₁-5
x₁(-x₁-5)=-150
-x₁²-5x₁=-150
x₁²+15x₁-10x₁+150=0
x₁(x₁+15)-10(x₁+15)=0
(x₁+15)(x₁-10)=0
x₁+15=0  x₁=-15
x₁-10=0  x₁=10