Răspuns:
Explicație pas cu pas:
Scrieti ecuatia de gradul II ce are solutiile :
a) x1=1 ,x2=-4 ⇒(x-x₁)(x-x₂)=0 ⇒(x-1)[x-(-4)]=0 ⇒(x-1)(x+4)=0
⇒x²-x+4x-4=0 ⇒x²+3x-4=0 Proba: Δ=9+16=25 x12=-3±5/2 x1=1; x2=-4
b) x1=-3,x2=-5 ⇒(x-x₁)(x-x₂)=0 ⇒(x+3)(x+5)=0 ⇒x²+3x+5x+15=0 ⇒x²+8x+15=0 ⇒Proba: Δ=64-60=4 ⇒x1,2=-8±2/2 x1=-4+1=-3 x2=-4-1=-5
c)x1=1+√2, x2=1-√2 ⇒(x-x₁)(x-x₂)=0 ⇒(x-1-√2)(x-1+√2)=0
⇒x²-x+x√2-x+1-√2-x√2+√2-2=0 ⇒x²-2x -1=0 Proba: Δ=4+4=8 x1,2=2±2√2/2 x1=1+√2 x2=1-√2
