Question

3x²-x+18=0x²-34x+289=0

Answer 1

3x^2-x+18=0

D = (-1)^2 - 4*3*18 = -215

D < 0

не имеет действительных корней

-

-

x²-34x+289=0

через полный квадрат

x²-2*17x+17²=0

(x - 17)² = 0

x - 17 = 0

x = 17

Answer 2

To solve the two quadratic equations given, we need to find the values of 'x' that satisfy each equation. We can use the quadratic formula for this purpose:

For a quadratic equation of the form ax² + bx + c = 0, the solutions for 'x' are given by:

x = (-b ± √(b² - 4ac)) / 2a

Let's solve each equation separately:

1. 3x² - x + 18 = 0

a = 3 b = -1 c = 18

Using the quadratic formula:

x = (1 ± √((-1)² - 4 * 3 * 18)) / 2 * 3 x = (1 ± √(1 - 216)) / 6 x = (1 ± √(-215)) / 6

Since the discriminant (b² - 4ac) is negative, there are no real solutions for this equation. The solutions involve complex numbers, which we can represent as:

x = (1 ± √215i) / 6

2. x² - 34x + 289 = 0

a = 1 b = -34 c = 289

Using the quadratic formula:

x = (34 ± √((-34)² - 4 * 1 * 289)) / 2 * 1 x = (34 ± √(1156 - 1156)) / 2 x = (34 ± √0) / 2

Since the discriminant (b² - 4ac) is zero, there is one real solution for this equation:

x = 34 / 2 x = 17

So, the solution to the second equation is:

x = 17

For the first equation, there are no real solutions, only complex solutions:

x = (1 ± √215i) / 6