Question

daca x1,x2 sunt radacinile ecuatiei x^2+x-1=0, sa se calculeze: a) x1+x2-2x1x2 b)1 supra x1 + 1 supra x2 c)x1^2+x2^2

Answer 1

x²+x-1=0
S=x1+x2= -1
P=x1*x2=c/a= -1
a) x1+x2-2x1*x2=  -1 -2*(-1)= 1
b) 1/x1+1/x2= x1*x2/x1+x2=  -1/-1 =1
c)x1²+x2²=S²-2P= 1-2*(-1)= 3