Question

giúp câu 2

Answer 1

2: ĐKXĐ: x<>-9

\(x^2+\frac{81x^2}{\left(x+9\right)^2}=40\)

=>\(x^2\left(x+9\right)^2+81x^2=40\left(x+9\right)^2\)

=>\(x^2\left(x^2+18x+81\right)+81x^2=40\left(x^2+18x+81\right)\)

=>\(x^4+18x^3+81x^2+81x^2=40x^2+720x+3240\)

=>\(x^4+18x^3+122x^2-720x-3240=0\)

=>\(x^4-2x^3-18x^2+20x^3-40x^2-360x+180x^2-360x-3240=0\)

=>\(\left(x^2-2x-18\right)\left(x^2+20x+180\right)=0\)

mà \(x^2+20x+180=\left(x+10\right)^2+80\ge80>0\forall x\)

nên \(x^2-2x-18=0\)

=>\(x^2-2x+1-19=0\)

=>\(\left(x-1\right)^2-19=0\)

=>\(\left(x-1\right)^2=19\)

=>\(\left[\begin{array}{l}x-1=\sqrt{19}\\ x-1=-\sqrt{19}\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\sqrt{19}+1\left(nhận\right)\\ x=-\sqrt{19}+1\left(nhận\right)\end{array}\right.\)