Question

X(x+4)-(x+4)=0 a(a-3)=2a-6

Answer 1

X(x+4)-(x+4)=0
x²+4x-x-4=0
x²+3x-4=0
a=1, b=3, c=-4
D=b²-4ac=9-4*1*(-4)=9+16=25
$x₁=\frac{-b+\sqrt{D} }{2a}= \frac{-3+5}{2} = \frac{2}{2}=1$
x₂= $\frac{-b- \sqrt{D} }{2a} = \frac{-3-5}{2}= \frac{-8}{2} = -4$
Ответ: (1;-4)
a(a-3)=2a-6
a²-3a=2a-6
a²-3a-2a+6=0
a²-5a+6=0
a=1, b=-5, c=6
D=b²-4ac= 25-4*1*6=25-24=1
x₁= $\frac{-b+ \sqrt{D} }{2a}= \frac{5+1}{2}= \frac{6}{2}= 3$
x₂= $\frac{-b- \sqrt{D} }{2a}= \frac{5-1}{2} = \frac{4}{2}=2$
Ответ: (3;2)

Answer 2

Let's solve each equation separately:

1. X(x + 4) - (x + 4) = 0

   To solve this equation, we can factor out the common factor of (x + 4):

   X(x + 4) - (x + 4) = 0 (x + 4)(X - 1) = 0

   Now, we have two possible solutions:

   1. x + 4 = 0 x = -4

   2. X - 1 = 0 X = 1

   So, the solutions are x = -4 and X = 1.

2. a(a - 3) = 2a - 6

   First, let's expand the left side of the equation:

   a(a - 3) = 2a - 6

   Now, distribute 'a' on the left side:

   a^2 - 3a = 2a - 6

   Next, let's move all the terms to one side to set the equation to zero:

   a^2 - 3a - 2a + 6 = 0

   Combine like terms:

   a^2 - 5a + 6 = 0

   Now, factor the quadratic equation:

   (a - 2)(a - 3) = 0

   Now, we have two possible solutions:

   1. a - 2 = 0 a = 2

   2. a - 3 = 0 a = 3

   So, the solutions are a = 2 and a = 3.