Question

gioi hạn \(\lim\limits_{x\rightarrow1}\dfrac{x+2-\sqrt{7x+2}}{x-\sqrt{5x-4}}=\dfrac{a}{b}\). (ps tôi giản) Tìm các gia trị thưc a,b?

Answer 1

\(\lim\limits_{x\rightarrow1}\dfrac{\left(x^2-3x+2\right)\left(x+\sqrt{5x-4}\right)}{\left(x^2-5x+4\right)\left(x+2+\sqrt{7x+2}\right)}=\lim\limits_{x\rightarrow1}\dfrac{\left(x-1\right)\left(x-2\right)\left(x+\sqrt{5x-4}\right)}{\left(x-1\right)\left(x-5\right)\left(x+2+\sqrt{7x+2}\right)}\)

\(=\lim\limits_{x\rightarrow1}\dfrac{\left(x-2\right)\left(x+\sqrt{5x-4}\right)}{\left(x-5\right)\left(x+2+\sqrt{7x+2}\right)}=\dfrac{1}{12}\)

\(\Rightarrow\left\{{}\begin{matrix}a=1\\b=12\end{matrix}\right.\)