Respuestas
Respuesta:
y una constante:
{\displaystyle f(x,y,z)=ax^{2}+by^{2}+cz^{2}+dxy+exz+fyz+gx+hy+iz+j,}{\displaystyle f(x,y,z)=ax^{2}+by^{2}+cz^{2}+dxy+exz+fyz+gx+hy+iz+j,}
con al menos uno de los coeficientes a, b, c, d, e o f de los términos de segundo grado que no son cero.
Una función cuadrática univariada (variable única) tiene la forma1
{\displaystyle f(x)=ax^{2}+bx+c,\quad a\neq 0}{\displaystyle f(x)=ax^{2}+bx+c,\quad a\neq 0}
{\displaystyle f(x,y)=ax^{2}+by^{2}+cxy+dx+ey+f\,\!}{\displacer f(x,y)=ax^{2}+bey^{2}+cxy+d+ey+f\,\!}
Explicación paso a paso:
Respuesta:
Ah
Explicación paso a paso:
II. Resuelva por el método de fórmula las siguientes ecuaciones.
a) x² - 3x - 10 = 0
= {- (-3) ±√[(-3)² - 4(1)(-10)]}/2
= [3 ±√(9 + 40)]/2
= (3 ±√49)/2
= (3 ± 7)/2
x₁ = -4/2 = -2
x₂ = 10/2 = 5
b) 7x² - 13x - 1 = 0
= {-(-13) ± √[(-13)² - 4(7)(-1)]}/2
= {13 ± √[169 + 28]}/2
= {13 ± √197}/2
= {13 ± √197}/2
x₁ = (13 + √197)/2
x₂ = (13 - √197)/2
c) 6x² + 7x - 3 = 0
= {-7 ± √[7² - 4(6)(-3)]}/2
= [-7 ± √(49 + 72)]/2
= (-7 ± √121)/2
= (-7 ± 11)/2
x₁ = 4/2 = 2
x₂ = -16/2 = -8
d) 9x² + 9x + 52 = 0
= {-9 ± √[9² - 4(9)(52)]}/2
= [-9 ± √81 - 1872]/2
x₁ = (-9 + √-1863)/2
x₂ = (-9 - √-1863)/2
e. mx² - nx + 1 = 0
= {-(-n) ± √[(-n)² - 4(m)(1)]}/2
= [n ± √(n² - 4m)]/2
x₁ = [n + √(n² - 4m)]/2
x₂ = [n - √(n² - 4m)]/2
f) x² - 4x - 117 = 0
= {-(-4) ± √[(-4)² - 4(1)(-117)]}/2
= {4 ± √[16 + 468]}/2
x₁ = {4 + 22}/2 = 13
x₂ = {4 + 22}/2 = -9
g) x² + 23x + 120 = 0
= {-23 ± √[23² - 4(1)(120)]}/2
= {-23 ± √[529 - 480]}/2
= {-23 ± √49}/2
x₁ = {-23 + 7}/2 = -16/2 = -8
x₂ = {-23 - 7}/2 = -30/2 = -15
h) 2x² + 3x - 65 = 0
= {-3 ± √[3² - 4(2)(-65)]}/2
= {-3 ± √[9 + 520]}/2
x₁ = {-3 + 23}/2 = 20/2 = 10
x₂ = {-3 - 23}/2 = -26/2 = -13
i) 4x² - 12x + 9 = 0
= {-(-12) ± √[(-12)² - 4(4)(9)]}/2
= {12 ± √[144 - 144]}/2
x₁; x₂ = = 12/2 = 6
j) 3x² + 5x - 2 = 0
= {-5 ± √[5² - 4(3)(-2)]}/2
= {-5 ± √[25 + 24]}/2
= {-5 ± 7}/2
x₁ = (- 5 - 7)/2 = -12/2 = -6
x₂ = (- 5 + 7)/2 = 2/2 = 1
III. Resuelva las siguientes ecuaciones:
a) 2x² + 32x = 0
x(2x + 32) = 0
x = 0 ∨ 2x + 32 = 0 → 2x = -32
C.S. = {0; -16)
b. 7x² - 56x = 0
x(7x - 56) = 0
x = 0 ∨ 7x - 56 = 0 → 7x = 56
C.S. = {0; 8}
c) x² - 7 = 0
x = √7
d) x² - 4x = 0
x(x - 4) = 0
C.S. = {0; 4}
e. 3x² = 4x
3x² - 4x = 0
x(3x - 4) = 0
C.S. = {0; 4/3)
f) 4x = x²
x² - 4x = 0
x(x - 4) = 0
C.S. = {0; 4}
g) 13x² = x
13x² - x = 0
x(13x - 1) = 0
C.S.= {0; 1/13}
h) 4x² - 108 = 0
x = √108/4 → (√9×√4×√3)/4 = 12√3/4 (≅ 2,59...)
i) 6x² - 3x = 0
x(6x - 3) = 0
C.S. = {0; 1/2}
j) 5x² - 180 = 0
x = √180/5 = 6√5/5
k) 5x² - 9x = 0
x(5x - 9) = 0
C.S. = {0; 9/5}
l) 6x² = 121
x = 11/6
Espero te ayude uwu