Question

[tex] \frac{x1 }{ x2} + \frac{x2 }{ x1}
[/tex]
stiiind ca x1 si x2 sunt radacinile ecuatiei $x^{2}+3x+4=0$

Answer 1

x1*x2=c/a=4
x1+x2=-b/a=-3
aducem expresia data la acelasi numitor⇔(x1^2+x2^2)x1*x2={(x1+x2)^2-2x1*x2}/x1*x2={(-3)^2-2*4}/4=9-8/4=1/4

Answer 2

x²+3x+4=0
x₁+x₂=-3
x₁x₂=4
x₁/x₂+x₂/x₁=(x₁²+x₂²)/x₁x₂=[(x₁+x₂)²-2x₁x₂]/x₁x₂=(9-8)/4=1/4