Question

Решите уравнение x^2-8x=727^2-8*727

Answer 1

х*(х-8)=727*(727-8)

х1=727 -корень . который виден сразу.

х*х-8х-727*(727-8)=0

по теореме Виета второй корень 8-727=-719

Ответ: два решения х=727 или х=-719

Answer 2

To solve the equation x^2 - 8x = 727^2 - 8 * 727, we first need to simplify the right-hand side of the equation:

727^2 - 8 * 727 = 528529 - 5816 = 522713.

Now, the equation becomes:

x^2 - 8x = 522713.

Next, we want to rearrange the equation into the standard quadratic form, which is ax^2 + bx + c = 0:

x^2 - 8x - 522713 = 0.

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

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a.

For our equation, a = 1, b = -8, and c = -522713. Substituting these values into the formula:

x = [ -(-8) ± √((-8)^2 - 4 * 1 * (-522713)) ] / 2 * 1 x = [ 8 ± √(64 + 2090852) ] / 2 x = [ 8 ± √2090916 ] / 2 x = [ 8 ± 1446.85 ] / 2.

Now, we have two possible solutions for x:

1. x = (8 + 1446.85) / 2 x = 1454.85 / 2 x ≈ 727.425.

2. x = (8 - 1446.85) / 2 x = -1438.85 / 2 x ≈ -719.425.

So, the two solutions to the equation are approximately x ≈ 727.425 and x ≈ -719.425.