Question

4x^2-5x-6=4(x-2)(x-a)

Answer 1

Ответ:

как можно решить уравнение с двумя неизвестными?

Пошаговое объяснение:

Answer 2

To solve the equation 4x^2 - 5x - 6 = 4(x - 2)(x - a), we need to find the values of 'x' that satisfy the equation. To do this, we'll expand the right-hand side (RHS) of the equation and then equate it with the left-hand side (LHS) to get a quadratic equation in standard form (ax^2 + bx + c = 0).

Let's expand the RHS first:

4(x - 2)(x - a) = 4(x^2 - ax - 2x + 2a) = 4(x^2 - (a + 2)x + 2a)

Now, our equation becomes:

4x^2 - 5x - 6 = 4(x^2 - (a + 2)x + 2a)

Now, equate the coefficients of corresponding powers of 'x':

1. Coefficient of x^2 on LHS = Coefficient of x^2 on RHS 4 = 4

2. Coefficient of x on LHS = Coefficient of x on RHS -5 = -(a + 2)

3. Constant term on LHS = Constant term on RHS -6 = 2a

Now, we can solve these equations to find the value of 'a':

From equation 3: -6 = 2a a = -6/2 a = -3

Now that we have the value of 'a', we can find the value(s) of 'x' by substituting 'a' back into equation 2:

From equation 2: -5 = -(a + 2) -5 = -(-3 + 2) -5 = -(1) -5 = -1

So, the value of 'x' is -1.

Therefore, the solution to the equation is 'a = -3' and 'x = -1'.