Question

Rezolvati urmatoarea functie de gradul 2:
$x^{2}$- (1+$\sqrt{2}$)$x$ + $\sqrt{2}$=0, x∈$Q$

Answer 1

Răspuns:

Explicație pas cu pas:

x²-(1+√2)x+√2=0

a=1

b=1+√2

c=√2

Δ=(1+√2)²-4√2=

1+2+2√2-4√2=1+2-2√2=

(√2-1)²

x1=[1+√2-√(√2-1)²]/2=

(1+√2-(√2-1)/2=

(1+√2-√2+1)/2=2/2=1

x2=[(1+√2)+√2-1)/2=

(1+√2+√2-1)/2=2√2/2=

√2