Question

Bai 1)Cho bieu thuc A=\(\frac{x+y-2\sqrt{xy}}{x-y}\)

a)Tim dieu kien de A co nghia

b)Rut gon A

c)Tinh A biet x=\(3+2\sqrt{2}\)va y=\(3-2\sqrt{2}\)

Bai 2) Cho bieu thuc B=\(\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\)

a)Tim dieu kien de B co nghia

b)Rut gon B

c) Tinh B voi x=\(4\left(2-\sqrt{3}\right)\)

d)Tim x de B co gia tri nho nhat

Answer 1

a) A có nghĩa\(\Leftrightarrow x-y\ne0\Leftrightarrow x\ne y\)

b) \(A=\frac{x+y-2\sqrt{xy}}{x-y}=\frac{\left(\sqrt{x-\sqrt{y}}\right)^2}{\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)}=\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}\)