Question

СРОЧНО!!! 30 БАЛЛОВ. 1/2 x² = -x +3 Решите и распишите!!!

Answer 1

$\displaystyle\bf\\\frac{1}{2} x^{2} =-x+3\\\\\\\frac{1}{2} x^{2} \cdot 2=-x\cdot 2+3\cdot 2\\\\\\x^{2} =-2x+6\\\\\\x^{2} +2x-6=0\\\\\\D=2^{2} -4\cdot(-6)=4+24=28=(2\sqrt{7} )^{2} \\\\\\x_{1} =\frac{-2-2\sqrt{7} }{2} =-1-\sqrt{7} \\\\\\x_{2} =\frac{-2+2\sqrt{7} }{2} =\sqrt{7} -1\\\\\\Otvet:-1-\sqrt{7} \ \ ; \ \ \sqrt{7} -1$

Answer 2

Solution for 1/2 x² = -x + 3

To solve the equation 1/2 x² = -x + 3, we can use the quadratic formula or factorization. Let's solve it step by step.

Using the Quadratic Formula

The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing the given equation 1/2 x² = -x + 3 to the standard form ax² + bx + c = 0, we have: - a = 1/2 - b = -1 - c = -3

Plugging these values into the quadratic formula gives us:

x = (-(-1) ± √((-1)² - 4(1/2)(-3))) / (2 * 1/2) x = (1 ± √(1 + 6)) / 1 x = (1 ± √7) / 1

So, the solutions for the equation 1/2 x² = -x + 3 are: x = (1 + √7) / 2 and x = (1 - √7) / 2.

Conclusion

The solutions for the equation 1/2 x² = -x + 3 are x = (1 + √7) / 2 and x = (1 - √7) / 2