Đặt x + 29 = a (a \(\ne-29;-30\))
Đề trở thành: \(\frac{1}{a^2}+\frac{1}{\left(a+1\right)^2}=\frac{5}{4}\)
\(\Leftrightarrow\frac{\left(a+1\right)^2+a^2}{a^2\left(a+1\right)^2}=\frac{5}{4}\)
\(\Leftrightarrow\frac{a^2+2a+1+a^2}{a^2\left(a^2+2a+1\right)}=\frac{5}{4}\)
\(\Leftrightarrow\frac{2a^2+2a+1}{a^4+2a^3+a^2}=\frac{5}{4}\)
\(\Leftrightarrow8a^2+8a+4=5a^4+10a^3+5a^2\)
\(\Leftrightarrow5a^4+10a^3-3a^2-8a-4=0\)
\(\Leftrightarrow5a^4+10a^3-3a^2-6a-2a-4=0\)
\(\Leftrightarrow5a^3\left(a+2\right)-3a\left(a+2\right)-2\left(a+2\right)=0\)
\(\Leftrightarrow\left(a+2\right)\left(5a^3-3a-2\right)=0\)
\(\Leftrightarrow\left(a+2\right)\left(5a^3-5a+2a-2\right)=0\)
\(\Leftrightarrow\left(a+2\right)\left(a-1\right)\left(5a^2+5a+2\right)=0\)
tới đây dễ r`
=\(\frac{1}{x^2}\)+ \(\frac{1}{^{29^2}}\)+\(\frac{1}{x^2}\)+\(\frac{1}{30^2}\)=5/4
=\(\frac{1}{x^2}\)x2 + \(\frac{1}{29^2}\)+\(\frac{1}{30^2}\)=5/4
=\(\frac{2}{x^2}\)+\(\frac{1}{841}\)+\(\frac{1}{900}\)=5/4
\(\frac{2}{x^2}\)=\(\frac{5}{4}\)-\(\frac{1}{841}\)-\(\frac{1}{900}\)bạn tự tính tiếp đi
