Question

(х+5)^2+(4-х)^2=2(х-4)(х+3)

Answer 1

Ответ:

Объяснение:

(х+5)^2+(4-х)^2=2(х-4)(х+3)=x²+10x+25+16-8x+x²=(2x-8)(x+3)=x²+10x+25+16-8x+x²=2x²+6x-8x-24=x²+10x+25+16+x²=2x²+6x-24=2x²+10x+41=2X²+6X-24=10X+41=6X-24=10X-6X=-24-41=4x=-65
x=$-\frac{65}{4}$

Answer 2

To solve the equation $(x + 5)^2 + (4 - x)^2 = 2(x - 4)(x + 3)$, you can follow these steps:

1. Expand the squares on the left-hand side of the equation:

$(x + 5)^2 = x^2 + 10x + 25$ $(4 - x)^2 = (4 - x)(4 - x) = 16 - 8x + x^2$

So, the equation becomes:

$x^2 + 10x + 25 + 16 - 8x + x^2 = 2(x - 4)(x + 3)$

2. Simplify and combine like terms:

$2x^2 + 2x + 41 = 2(x - 4)(x + 3)$

3. Expand the right-hand side of the equation:

$2(x - 4)(x + 3) = 2(x^2 - x - 12) = 2x^2 - 2x - 24$

So, the equation now looks like:

$2x^2 + 2x + 41 = 2x^2 - 2x - 24$

4. Subtract $2x^2$ from both sides to eliminate the $2x^2$ terms:

$2x + 41 = -2x - 24$

5. Add $2x$ to both sides to isolate the $x$ terms on one side:

$4x + 41 = -24$

6. Subtract 41 from both sides to solve for (x:

$4x = -24 - 41$ $4x = -65$

7. Finally, divide by 4 to find the value of (x:

$x = -65 / 4$

So, the solution to the equation is $x = -65/4$.