Question

X²+6X-6=0. 4(2x-1)*3(3x+2)>1

Answer 1

Ответ:

x²+6x-6=0

Объяснение:

D=b²-4ac = 6²-4*1*(-6)=36+24=60

Answer 2

It seems you have two separate equations or expressions. Let's break down each one:

1. Quadratic Equation: x² + 6x - 6 = 0

This is a quadratic equation in the form of ax² + bx + c = 0. In your case, a = 1, b = 6, and c = -6. You can solve this equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Plugging in the values:

x = (-6 ± √(6² - 4(1)(-6))) / (2(1)) x = (-6 ± √(36 + 24)) / 2 x = (-6 ± √60) / 2 x = (-6 ± 2√15) / 2

This gives you two solutions for x:

x = (-6 + 2√15) / 2 x = -3 + √15

x = (-6 - 2√15) / 2 x = -3 - √15

2. Inequality: 4(2x - 1) * 3(3x + 2) > 1

To solve this inequality, you can simplify and solve for x:

4(2x - 1) * 3(3x + 2) > 1

12x^2 - 12x + 24x + 16 > 1

12x^2 + 12x + 16 > 1

12x^2 + 12x + 15 > 0

This quadratic expression is greater than 0 when its discriminant is negative (since the coefficient of the x^2 term is positive). To find the values of x that satisfy this inequality, you can use the quadratic formula again:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 12, b = 12, and c = 15. Plugging in these values:

x = (-12 ± √(12² - 4(12)(15))) / (2(12)) x = (-12 ± √(144 - 720)) / 24 x = (-12 ± √(-576)) / 24

Since the discriminant is negative, you get complex solutions:

x = (-12 ± 24i√6) / 24 x = -0.5 ± i√6

This means that there are no real values of x that satisfy the inequality.

To summarize, the solutions for the quadratic equation x² + 6x - 6 = 0 are x = -3 + √15 and x = -3 - √15. The inequality 4(2x - 1) * 3(3x + 2) > 1 does not have real solutions for x.