Question

X^2+2(a-2)x-8a=0 .....................

Answer 1

Ответ:

x=4; a=-2

Пошаговое объяснение:

x^2+(2a-4)x-8a=0 ||вносим в скобки 2

D=4a^2-16a+16+32a=4a^2+16a+16

4a^2+16a+16>=0 ||Находим параметр а

D=256-256=0

a= -16/8= -2

x^2-8x+16=0  ||Вводим значение параметра а

D=64-64=0 || Находим параметр x

x=8/2=4

Answer 2

The given equation is:

X^2 + 2(a - 2)x - 8a = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Comparing the given equation to the standard form ax^2 + bx + c = 0, we have: a = 1 b = 2(a - 2) c = -8a

Let's substitute these values into the quadratic formula and simplify:

x = (-(2(a - 2)) ± √((2(a - 2))^2 - 4(1)(-8a))) / (2(1)) x = (-2a + 4 ± √(4(a - 2)^2 + 32a)) / 2 x = (-2a + 4 ± √(4(a^2 - 4a + 4) + 32a)) / 2 x = (-2a + 4 ± √(4a^2 - 16a + 16 + 32a)) / 2 x = (-2a + 4 ± √(4a^2 + 16a + 16)) / 2 x = (-2a + 4 ± √((2a + 4)^2)) / 2 x = (-2a + 4 ± 2(a + 2)) / 2 x = -a + 2 ± (a + 2) x = -a + 2 + a + 2 or x = -a + 2 - (a + 2)

Simplifying further:

x = 4 or x = -2a

Therefore, the solutions to the quadratic equation X^2 + 2(a - 2)x - 8a = 0 are:

x = 4 x = -2a