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formati ecuatia de gradul al 2 lea daca x1=2+ radical 2 si x2=2- radical 2​

Răspuns :

Bună!

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x₁; x₂ ∈ R

S=x₁+x₂

P=x₁*x₂

x²-Sx+P=0

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[tex]\left \{ {x_{1}=2+\sqrt{2} } \atop {x_{2}=2-\sqrt{2} }} \right. => S=4, P=2[/tex]

[tex]S=2+\sqrt{2} +2-\sqrt{2} =2+2=4[/tex]

[tex]P=(2+\sqrt{2} )(2-\sqrt{2} )=2^{2} -(\sqrt{2})^{2} =4-2=2[/tex]

x²-Sx+P ⇒ x²-4x+2