Question

2. Se considera ecuatia 2x² - 10x + 1 = 0 si x1 si x2 radacinile ecuatiei
Calculati
a)1supra x1 + 1 supra x2
b) (x1+2)² + (x2 +2)²
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Answer 1

Răspuns:

Explicație pas cu pas:

2x² - 10x + 1 = 0

a)1/x1+1/x2=(x1+x2)/x1x2=S/P

S=10/2=5   P=1/2       ⇒ 1/x1+1/x2=5/1/2=10

b)(x1+2)² + (x2 +2)² =x1²+4x1+4+x2²+4x2+0=x1²+x2²+4(x1+x2)+8

x1²+x2²=(x1+x2)²-2x1x1=S²-2P

(x1+2)² + (x2 +2)² =S²-2P+4S+8=25-2/2+20+8=25-1+20+8=52