Question

(х-3)²+(x+4)²-(x-5)²=17x +24​

Answer 1

Надеюсь все понятно, удачи)

Answer 2

To solve the equation $(x - 3)^2 + (x + 4)^2 - (x - 5)^2 = 17x + 24$, you can start by expanding and simplifying the left side of the equation, and then solving for $x$.

Here's the expanded form:

$(x - 3)^2 + (x + 4)^2 - (x - 5)^2 = 17x + 24$

Expanding the squares:

$(x^2 - 6x + 9) + (x^2 + 8x + 16) - (x^2 - 10x + 25) = 17x + 24$

Now, simplify and combine like terms:

$(x^2 - 6x + 9) + (x^2 + 8x + 16) - (x^2 - 10x + 25) = 17x + 24$

Now, distribute the negative sign in front of the third term on the left side:

$x^2 - 6x + 9 + x^2 + 8x + 16 - x^2 + 10x - 25 = 17x + 24$

Simplify further:

$x^2 - 6x + 9 + x^2 + 8x + 16 - x^2 + 10x - 25 = 17x + 24$

Combine like terms:

$x^2 + x^2 - x^2 - 6x + 8x + 10x + 9 + 16 - 25 = 17x + 24$

Now, simplify the equation:

$9x = 24$

Now, solve for $x$:

$x = \frac{24}{9} = \frac{8}{3}$

So, the solution to the equation $(x - 3)^2 + (x + 4)^2 - (x - 5)^2 = 17x + 24$ is $x = \frac{8}{3}$.

Answer 3

To solve this equation, you can start by expanding and simplifying the expressions on both sides:

(х-3)² + (x+4)² - (x-5)² = 17x + 24

First, expand the squares:

(x² - 6x + 9) + (x² + 8x + 16) - (x² - 10x + 25) = 17x + 24

Now, simplify further by combining like terms:

x² - 6x + 9 + x² + 8x + 16 - x² + 10x - 25 = 17x + 24

Now, simplify the equation:

x² - 6x + 9 + x² + 8x + 16 - x² + 10x - 25 - 17x - 24 = 0

Now, combine like terms again:

2x² - 6x + 9 + 8x - 10x - 25 - 17x - 24 = 0

Now, combine like terms:

2x² - 25x - 40 = 0

Now, you have a quadratic equation in the form ax² + bx + c = 0, where a = 2, b = -25, and c = -40. You can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values:

x = (-(-25) ± √((-25)² - 4(2)(-40))) / (2(2))

x = (25 ± √(625 + 320)) / 4

x = (25 ± √945) / 4

Now, you can simplify further:

x = (25 ± 3√105) / 4

So, the solutions to the equation are:

x = (25 + 3√105) / 4 and x = (25 - 3√105) / 4