Question

Не розв*язуючи +12х+6=0, знайдіть значення виразу х₁²+х₂², де х₁, х₂- корені цього рівняння. РОЗВ*ЯЗКИ ТАКОЖ ПИШІТЬ БУДЬ ЛАСКА.

Answer 1

X1+x2=12 U x1*x2=6
x1²+x2²=(x1+x2)²-2x1*x2=12²-2*6=144-12=132

Answer 2

Solving the Equation 12x + 6 = 0

To solve the equation 12x + 6 = 0, we can start by subtracting 6 from both sides of the equation to isolate the term with x. Then, we can divide both sides by 12 to solve for x.

Subtract 6 from both sides: 12x + 6 - 6 = 0 - 6 12x = -6

Divide both sides by 12: 12x / 12 = -6 / 12 x = -1/2

Finding the Value of the Expression x₁² + x₂²

Now that we have found the value of x, which is -1/2, we can find the value of the expression x₁² + x₂², where x₁ and x₂ are the roots of the equation 12x + 6 = 0.

The sum of the squares of the roots of a quadratic equation can be found using the following formula: x₁² + x₂² = (x₁ + x₂)² - 2x₁x₂

In this case, since the equation 12x + 6 = 0 has only one root, the value of x₁ and x₂ is the same, which is -1/2.

Substitute the value of x into the formula: x₁² + x₂² = (-1/2)² + (-1/2)² x₁² + x₂² = 1/4 + 1/4 x₁² + x₂² = 1/2

Therefore, the value of the expression x₁² + x₂², where x₁ and x₂ are the roots of the equation 12x + 6 = 0, is 1/2.