Question

Solución de ecuaciones completando cuadrados

x² + 4x + 3 = 0

x² - 6x + 5 = 0

x² - 6x - 7 = 0

x² - 8x + 16 = 0

x² + 2x - 2 = 0

x² - 4x + 2 = 0

x² + 5x + 5 = 0

x² + x - 1 = 0

Ayuda :'>

es para dentro de unas horas

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Answer 1

Respuesta:

Explicación paso a paso:

x² + 4x + 3 = 0

x²+4x=-3   (completamos trinomio cuadrado perfecto)

x²+4x+4=-3+4

(x+2)²=1

x+2=√1

x=-2±1

x₁=-1

x₂=-3

-----------------------------

x² - 6x + 5 = 0

x²-6x=-5

x²-6x+9=-5+9

(x-3)²=4

x-3=√4

x=3±2

x₁=5

x₂=1

---------------------------

x² - 6x - 7 = 0

x²-6x=7

x²-6x+9=7+9

(x-3)²=16

x-3=√16

x=3±4

x₁=7

x₂=-1

--------------------------------------

x² - 8x + 16 = 0

x² - 8x+16=0  (es trinomio cuadrado perfecto)

(x-4)²=0

(x-4)(x-4)=0

x-4=0

x=4

------------------------------

x² + 2x - 2 = 0

x² + 2x = 2

x²+2x+1=2+1

(x+1)²=3

x+1=√3

x=1±√3

x₁=1+√3

x₂=1-√3

-------------------------

x² - 4x + 2 = 0

x²-4x=-2

x²-4x+4=-2+4

(x-2)²=2

x-2=√2

x=2±√2

x₁=2+√2

x₂=2-√2

-----------------------------------

x² + 5x + 5 = 0

x²+5x+(2,5)²=-5+(2,5)²

(x+2,5)²=-5+6,25

(x+2,5)²=1,25

x+2,5=√1,25

x=-2,5±√1,25

x₁=-2,5+√1,25

x₂=-2,5-√1,25

-------------------------------

x² + x - 1 = 0

x² + x=-1

x²+x+1/4=-1+1/4

(x+1/2)²=-3/4

x+1/2 =-√3/2

x=-1/2-√3/2

x₁=(-1-√3)/ 2

x²=(-1+√3 )/2