Question

Решите уравнение: (m^2 - 36)^2 + (m^2 - 2m - 24)^2 = 0

Answer 1

$(m^2-36)^2+(m^2-2m-24)^2=0\\(m^2-6^2)^2+((m-1)^2-5^2)^2=0\\((m-6)(m+6))^2+((m-1-5)(m-1+5))^2=0\\((m-6)(m+6))^2+((m-6)(m+4))^2=0\\(m-6)^2((m+6)^2+(m+4)^2)=0\\\\m-6=0\\m=6\\\\(m+6)^2+(m+4)^2=0\\m^2+8m+16+m^2+12m+36=0\\2m^2+20m+52=0 \:\: |:2\\m^2+10m+26=0\\D=100-104=-4 < 0 \Rightarrow \:x\in \varnothing (x \neq \mathbb{R})$

Ответ: x = 6

Answer 2

To solve the equation, we need to find the value of "m" that satisfies the equation:

(m^2 - 36)^2 + (m^2 - 2m - 24)^2 = 0

First, we can simplify the equation:

(m^2 - 36)^2 + (m^2 - 2m - 24)^2 = 0 m^4 - 72m^2 + 36^2 + (m^2 - 2m - 24)^2 = 0 m^4 - 72m^2 + 1296 + (m^2 - 2m - 24)^2 = 0

Now let's expand the second term:

(m^2 - 2m - 24)^2 = (m^2 - 2m - 24)(m^2 - 2m - 24) = m^4 - 2m^3 - 24m^2 - 2m^3 + 4m^2 + 48m - 24m^2 + 48m + 576 = m^4 - 4m^3 - 46m^2 + 96m + 576

Substitute this back into the original equation:

m^4 - 72m^2 + 1296 + (m^4 - 4m^3 - 46m^2 + 96m + 576) = 0 2m^4 - 4m^3 - 118m^2 + 96m + 1872 = 0

Now, let's try to factorize if possible:

2m^4 - 4m^3 - 118m^2 + 96m + 1872 = 0

There is no simple way to factorize this equation further. So, we may need to use numerical methods to approximate the solutions.

One possible method is to use a numerical solver or graphing calculator to find the roots of the equation. By plotting the graph of the equation, we can estimate the values of "m" where the equation equals zero.

Without a numerical solver or graphing calculator, it is challenging to find exact solutions for this equation. However, approximate solutions can be found using numerical methods. If you have access to such tools, you can input the equation and find the solutions.