Question

Câu 2 Cho biểu thức P=\(\left(\sqrt{x}+1\right)^2-\dfrac{2x+6\sqrt{x}}{\sqrt{x}+3}\)

a Rút gọn biểu thức P

b Tìm x sao cho P có giá trị là 2013

Answer 1

ĐK: \(x\ge0\)

a, \(P=\left(\sqrt{x}+1\right)^2-\dfrac{2x+6\sqrt{x}}{\sqrt{x}+3}\)

\(=\left(\sqrt{x}+1\right)^2-\dfrac{2\sqrt{x}\left(\sqrt{x}+3\right)}{\sqrt{x}+3}\)

\(=\left(\sqrt{x}+1\right)^2-2\sqrt{x}\)

\(=x+2\sqrt{x}+1-2\sqrt{x}=x+1\)

b, \(P=2013\Leftrightarrow x+1=2013\Leftrightarrow x=2012\left(TM\right)\)

Answer 2

a) \(P=\left(\sqrt{x}+1\right)^2-\dfrac{2x+6\sqrt{x}}{\sqrt{x}+3}\)

\(P=x+2\sqrt{x}+1-\dfrac{2\sqrt{x}\left(\sqrt{x}+3\right)}{\sqrt{x}+3}\\ P=x+2\sqrt{x}+1-2\sqrt{x}\\ P=x+1\)

b) \(P=2013\Rightarrow x+1=2013\Rightarrow x=2013-1=2012\)

Vậy \(x=2012\) thì P có giá trị là 2013