Question

Rezolvati in R ecuatiile : a)2x la puterea a 2 - x + 2 =0 b) x la puterea a 2 - 4x +4=0

Answer 1

Răspuns:

Explicație pas cu pas:

a)2x²-x+2=0⇒  Δ=1-4×4<0  ecuatia nu are solutii reale

b)x²-4x+4=(x-2)²   ecuatia are solutie unica  x=2    Δ=16-16=0

Answer 2

$\it a)\ 2x^2-x+2=0|_{\cdot2} \Rightarrow 4x^2-2x+4=0 \Rightarrow 3x^2+x^2-2x+1+3=0 \Rightarrow \\ \\ \Rightarrow 3x^2+3+(x-1)^2=0\ \ \ \ \ (*)\\ \\ 3x^2+3>0,\ \ (x-1)^2\geq0 \stackrel{(*)}{\Longrightarrow}\ ecua\c{\it t}ie\ imposibil\breve{a} \Rightarrow S=\varnothing\\ \\ \\ b)\ x^2-4x+4=0 \Leftrightarrow(x-2)^2=0 \Leftrightarrow x=2$