Question

Rezolvati ecuatiile :
x^2+10=0
x^2-5x=0
2x^2=0
2x^2+3x-5=0
x^2-5x+6=0

Answer 1

Răspuns:

x² + 10 = 0

x² = -10

x = ±√-10

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x² - 5x = 0

a = 1 b = -5 c = 0

∆ = b² - 4ac

∆ = 25 - 0

∆ = 25 > 0

x1 = (-b + √∆)/2a

x1 = (5 + 5)/2

x1 = 10/2

x1 = 5

x2 = (-b - √∆)/2a

x2 = (5 - 5)/2

x2 = 0/2

x2 = 0

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2x² = 0

x² = 0

x = 0

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2x² + 3x - 5 = 0

a = 2 / b = 3 / c = -5

∆ = b² - 4ac

∆ = 9 - 4 × 2 × -5

∆ = 9 + 40

∆ = 49

x1 = (-b + √∆)/2a

x1 = (-3 + 7)/4

x1 = 4/4

x1 = 1

x2 = (-b - √∆)/2a

x2 = (-3 - 7)/4

x2 = -10/4

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x² - 5x + 6 = 0

a = 1 / b = -5 / c = 6

∆ = b² - 4ac

∆ = 25 - 24

∆ = 1

x1 = (-b + √∆) /2a

x1 = (5 + 1)/2

x1 = 6/2

x1 = 3

x2 = (-b - √∆)/2a

x2 = (5 - 1)/2

x2 = 4/2

x2 = 2

Answer 2

1. x²+10=0⇒x²= -10⇒x=±√-10⇒x=√10

2.x²-5x=0 Calculam delta: a=1, b=-5, c=0

Δ=b²-4ac=-5²-4*1*0

Δ=25-0=25

$x_{1,2}$=-b±√Δ /2*a=5±5/2⇒

$x_{1} =5+5/2=10/2=5\\x_{2} =5-5/2=0/2=0$

2. 2x²=0⇒x²=0/2=0⇒x=0

3. 2x²+3x-5=0 Calculam Delta    a=2, b=3, c=-5

Δ=3²+4*2*5=9+40=49

$x_{1} =-3+7/4=4/4=1\\x_{2} =-3-7/4=-10/4=-5/2$  simplificam prin 2

4. x²-5x+6=0 Calculam Delta  a=1, b=-5 c=6

Δ=-5²-4*1*6=25-24=1

scrieti voi formula la x1,2

$x_{1} =5+1/2=6/2=3\\x_{2} =5-1/2=4/2=2$