Question

x²-2x-6=0

3. 5m²-2m-16=0

4. 8y²-7y+2=0

5. 11y²+4y-2=0

6. 16x²+5x-19=0

7. 20z²-18z-16=0

8. 15x²+17x-5=0​

Answer 1

Răspuns:

Explicație pas cu pas:

1) x²-2x-6=0

x1,2=(1±√1+6)   ⇒x1=1+√7   si x2=1-√7

x²-2x-6=(x-1-√7)(x-1+√7

3. 5m²-2m-16=0  

m1,2=(1±√1+5·16)/5=(1±√81)/5=(1±9/)5   ⇒

m1=10/5=2     si m2=-8/5

5m²-2m-16=(x-2)(5m+8)

4. 8y²-7y+2=0

x1,2=(7±√49-64)/16   ⇒Δ negativa    nu are solutii reale

5. 11y²+4y-2=0

x1,2=(-2±√4+22)/11=(-2±√26)/11=

x1=(√26-2)/11      si x2=-(√26+2)/11

6. 16x²+5x-19=0

x1,2=(-5±√25+4·16·19)/32=(-5±√1241)/32

x1≈(-5+35)/32=30/32=15/16     x2≈(-5-35)/32=-40/32=-5/8

7. 20z²-18z-16=0  

z1,2=(9±√81+20·16)/20=(9±√401)/20

z1≈(9+20)/20=29/20      2≈(9-20)/20=-11/20

8. 15x²+17x-5=0​

x1,2=(-17±√289+20·15)/4·15=(-17±√589)/60