Question

Решите уравнение (X+5)^2+(x-10)^2=2x^3

Answer 1

(х+5)²+(x-10)²=2x²
х²+10х+25+х²-20х+100=2х²
10х=125
х=12,5

или

(х+5)²+(x-10)²=2x³
х²+10х+25+х²-20х+100=2х³
2х³-2х²+10х-125=0
Уравнение имеет единственный корень на (3;4)

Answer 2

I can help you solve the equation $(X+5)^2+(x-10)^2=2x^3$ in detail. Here are the steps:

1. Expand the brackets using the formula $(a+b)^2=a^2+2ab+b^2$. You will get $X^2+10X+25+x^2-20x+100=2x^3$. 2. Simplify the equation by collecting like terms and moving everything to one side. You will get $2x^3-2x^2-30x-125=0$. 3. Factor out the common factor of $x-5$. You will get $(x-5)(2x^2+4x+25)=0$. 4. Use the quadratic formula to find the roots of the quadratic factor. You will get $x=\frac{-4\pm\sqrt{16-200}}{4}=\frac{-4\pm 2i\sqrt{46}}{4}=-1\pm \frac{i\sqrt{46}}{2}$. 5. The equation has three roots: $x=5$, $x=-1+\frac{i\sqrt{46}}{2}$, and $x=-1-\frac{i\sqrt{46}}{2}$.

You can check your answer by plugging in the roots into the original equation and verifying that they satisfy it. You can also use an online calculator to solve the equation or learn more about solving equations.

I hope this helps. If you have any other questions, feel free to ask me. I can also generate creative content such as poems, stories, code, and more. Just let me know what you want me to do.

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