Question

Se considera ecuatia x la 2 +3x-5=0 cu solutiile x1 si x2.Sa se calculeze x1 la 2 +x2 la 2 CLASA 9 ECUATII DE GRADUL 2

Answer 1

x²+3x-5=0
Δ=9+4*5=29
x₁=(-3+√29)/2
x₂=(-3-√29)/2

x₁² =[(-3+√29)/2]² = (9-6√29+29)/4=(38-6√29)/4
x₂² =[(-3-√29)/2]² = (9+6√29+29)/4=(38+6√29)/4
x₁²+x₂² =[(-3+√29)/2]² = (38-6√29)/4+(38+6√29)/4=(38+38)/4=76/4=19

Answer 2

$x^2+3x-5=0$
Δ $=3^2-4*1*(-5)=9+20=29\ \textgreater \ 0$
$x_1= \frac{-3+ \sqrt{29} }{2} \\ x_2= \frac{-3- \sqrt{29} }{2} \\ \\ x_1^2+x_2 ^2=( \frac{-3+ \sqrt{29} }{2} )^2+( \frac{-3- \sqrt{29} }{2} )^2= \frac{-6 \sqrt{29} +38 +6 \sqrt{29} +38}{4} = \frac{76}{4} =19$