Question

Решите уравнение (х-2)(-х-1)=0 Если уравнение имеет одного корня, в ответе запишите меньший из корней

Answer 1

(x-2)(-x-1)=0
-x-x+2x+2=0
-x-x+2x=0-2
0x=-2
Вроде так

Answer 2

Solving the Equation (х-2)(-х-1)=0

To solve the equation (х-2)(-х-1)=0, we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero.

First, let's expand the given equation: (х-2)(-х-1)=0

Expanding the equation gives us: -х^2 + х + 2х - 2 = 0

Simplifying further: -х^2 + 3х - 2 = 0

Now, we can solve for the roots of the equation.

Finding the Roots

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -1, b = 3, and c = -2. Substituting these values into the quadratic formula gives us: x = (-3 ± √(3^2 - 4*(-1)*(-2))) / (2*(-1))

Solving for x: x = (-3 ± √(9 - 8)) / (-2) x = (-3 ± √1) / (-2) x = (-3 + 1) / (-2) or x = (-3 - 1) / (-2) x = -2 / (-2) or x = -4 / (-2) x = 1 or x = 2

Conclusion

The roots of the equation (х-2)(-х-1)=0 are x = 1 and x = 2. Since the question asks for the smaller of the two roots, the answer is x = 1.