Question

Câu 1: Phân tích thành nhân tử:

a) \(A=x-2\sqrt{3}+3\) với \(x\ge0\)

b) \(B=x+2\sqrt{x}-3\) với \(x\ge0\)

c) \(C=x\sqrt{x}-1\) với \(x>0\)

d) \(D=2x-3\sqrt{xy}-5y\) với \(x\ge0\), \(y\ge0\)

Câu 2: Cho \(\sqrt{3-x}+\sqrt{5-x}-2\)

Hãy tính \(A=\sqrt{3-x}-\sqrt{5-x}\)

Answer 1

Câu 1 :

a, Ta có : \(A=x-2\sqrt{3}+3\)

\(=x-\sqrt{3}\left(2-\sqrt{3}\right)\)

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

b, Ta có : \(B=x+2\sqrt{x}-3\)

\(=x+2\sqrt{x}+1-4=\left(\sqrt{x}+1\right)^2-4\)

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

c, Ta có : \(C=x\sqrt{x}-1\)

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

d, Ta có : \(D=2x-3\sqrt{xy}-5y\)

\(=2x+2\sqrt{xy}-5\sqrt{xy}-5y\)

\(=2\sqrt{x}\left(\sqrt{x}+\sqrt{y}\right)-5\sqrt{y}\left(\sqrt{x}+\sqrt{y}\right)\)

\(=\left(\sqrt{x}+\sqrt{y}\right)\left(2\sqrt{x}-5\sqrt{y}\right)\)