Question

Am nevoie de ajutor vă rog^^​

Answer 1

Răspuns:

(29+3√5)/10

Explicație pas cu pas:

x²-x-1 = 0

x₁,₂ = (1±√5)/2

x₁ = (1-√5)/2  ; x₂ =  (1+√5)/2

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x₁² = [(1-√5)/2]² = (1-2√5+5)/4 = (6-2√5)/4 = (3-√5)/2

x₂² =  [(1+√5)/2]² = (1+2√5+5)/4 = (6+2√5)/4 = (3+2√5)/2

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a = (x₁²+3x₁-2)/(x₁²-2x₁+2)=

[(3-√5)/2+3(1-√5)/2-²⁾2]/[(3-√5)/2-2(1+√5)/2+²⁾2]=

= (3-√5+3-3√5-4)/(3-√5-2-2√5+4) = (2-4√5)/(5-3√5) =

= (2-4√5)(5+3√5)/[(5-3√5)(5+3√5)] =

=(10+6√5-20√5-12·5)/(25+15√5-15√5-9·5) =

= (-50-14√5)/(-20) = (25-7√5)/10

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b = (x₂²+3x₂-2)/(x₂²-2x₂+2)=

=[(3+2√5)/2 +3(1+√5)/2 - ²⁾2]/[(3+2√5)/2-2(1+√5)/2+²⁾2] =

= (3+2√5+3+3√5-4)/(3+2√5-2-2√5+4) =

= (2+5√5)/5

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a+b = (25-7√5)/10 +  ²⁾(2+5√5)/5 =

= (25-7√5+4+10√5)/10 = (29+3√5)/10