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