ĐKXĐ : \(x\ne\pm6\)
\(\frac{36}{x+6}+\frac{36}{x-6}=\frac{9}{2}\)
\(\frac{72\left(x-6\right)}{\left(x+6\right)\left(x-6\right)2}+\frac{72\left(x+6\right)}{\left(x-6\right)\left(x+6\right)2}=\frac{9\left(x+6\right)\left(x-6\right)}{2\left(x+6\right)\left(x-6\right)}\)
\(72\left(x-6\right)+72\left(x+6\right)=9\left(x+6\right)\left(x-6\right)\)
\(72x-432+72x+432=9x^2-324\)
\(144x=9x^2-324\)
\(144x-9x^2+324=0\)
\(-9x^2+144x+324=0\)
\(\Delta=144^2-4.\left(-9\right).324=32400>0\)
Nên phương trình có 2 nghiệm phân biệt
\(x_1=\frac{-144-\sqrt{32400}}{2.\left(-9\right)}=\frac{-144-180}{-18}=18\)
\(x_2=\frac{-144+\sqrt{32400}}{2.\left(-9\right)}=\frac{-144+180}{-18}=-2\)
Đk : x khác 6 và -6
\(\frac{36}{x+6}+\frac{36}{x-6}=\frac{9}{2}\)
\(< =>\frac{36\left(x-6\right)+36\left(x+6\right)}{\left(x+6\right)\left(x-6\right)}=\frac{9}{2}\)
\(< =>\frac{36x-216+36x+216}{x^2-6x+6x-36}=\frac{9}{2}\)
\(< =>\frac{72x}{x^2-6^2}=\frac{9}{2}\)
\(< =>144x=9x^2-324\)
\(< =>9x^2-144x-324=0\)
Ta có : \(\Delta=\left(-144\right)^2-4.9.\left(-324\right)=32400\)
\(< =>\sqrt{\Delta}=180\)
Vì delta > 0 nên pt có 2 nghiệm phân biệt
\(x_1=\frac{144+180}{18}=18\)
\(x_2=\frac{144-180}{18}=-2\)
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