Question

Ma poate ajuta cineva va rog. Mulțumesc!

Answer 1

c) ec x²-Sx+P=0

S=x1+x2= -2+5=3

P=x1*x2= -2*5= -10

ec: x²-3x-10=0

d) amplificam pe prima fractie cu x2 si pe cealalta cu x1

1/(x1*x2)=1/5

x1*x2=c/a= -5/-1=5

Answer 2

$\displaystyle c.~~ax^2+bx+c=0~~~~~~~~~~~~~~~~x_1=-2,~x_2=5\\ \\ x^2-Sx+P=0\\ \\ S=x_1+x_2 \Rightarrow S=-2+5 \Rightarrow S=3 \\ \\ P=x_1x_2 \Rightarrow P=(-2) \cdot 5 \Rightarrow P=-10\\ \\ \mathbf{x^2-3x-10=0}\\ \\ d.~~-x^2+2x-5=0 \\ \\ \frac{1}{x_1} +\frac{1}{x_2} =\frac{x_1+x_2}{x_1x_2}=\frac{S}{P}\\ \\ a=-1,~b=2,~c=-5\\ \\ S=x_1+x_2=-\frac{b}{a} =-\frac{2}{-1} =2\\ \\ P=x_1x_2=\frac{c}{a} =\frac{-5}{-1} =5 \\ \\ \mathbf{\frac{1}{x_1} +\frac{1}{x_2} =\frac{2}{5} }$