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Leontine
@Leontine
April 2019
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8 points !
J'ai besoin d'aide pour résoudre cette équation svp
(x² - 5x)² = x² - 5x + 42
On pourra effectuer un changement de variable
Merci d'avance !
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caylus
Verified answer
Bonjour,
Soit y=x²-5x
y²=y+42
y²-y-42=0
Δ=1+4*42=169=13²
y1=(1+13)/2=7
y2=(1-13)/2=-6
1) si y=7 alors 7=x²-5x
x²-5x-7=0
Δ=25+4*7=√53
x1=(5+√53)/2
x2=(5-√53)/2
2)si y=-6 alors -6=x²-5x
x²-5x+6=0
Δ=25-4*6=1
x1=(5+1)/2=3
x2=(5-1)/2=2
sol={2,3,(5-√53)/2,(5+√53)/2 }
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Verified answer
Bonjour,Soit y=x²-5x
y²=y+42
y²-y-42=0
Δ=1+4*42=169=13²
y1=(1+13)/2=7
y2=(1-13)/2=-6
1) si y=7 alors 7=x²-5x
x²-5x-7=0
Δ=25+4*7=√53
x1=(5+√53)/2
x2=(5-√53)/2
2)si y=-6 alors -6=x²-5x
x²-5x+6=0
Δ=25-4*6=1
x1=(5+1)/2=3
x2=(5-1)/2=2
sol={2,3,(5-√53)/2,(5+√53)/2 }