Question

Giải phương trình:

a)\(\dfrac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

b)\(\dfrac{a-b+a\sqrt{b}-b\sqrt{a}}{\sqrt{b}+\sqrt{a}+\sqrt{ab}}\)

c)\(\sqrt{\dfrac{1}{b}+\dfrac{1}{b^2}}\)

Answer 1

a) \(\dfrac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)

\(=\dfrac{\sqrt{x}\sqrt{y}\cdot\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}\)

\(=\sqrt{x}\sqrt{y}\)

\(=\sqrt{xy}\)

Answer 2

c) \(\sqrt{\dfrac{1}{b}+\dfrac{1}{b^2}}\) = \(\sqrt{\dfrac{1}{b}+\dfrac{1}{b.b}}\) = \(\sqrt{\dfrac{b+1}{b^2}}\) = \(\dfrac{\sqrt{b+1}}{b}\)

đề phải gi là gút gọn biểu thức mới đúng

Answer 3

b) \(\dfrac{a-b+a\sqrt{b}-b\sqrt{a}}{\sqrt{b}+\sqrt{a}+\sqrt{ab}}\) = \(\dfrac{\left(a-b\right)+\left(a\sqrt{b}-b\sqrt{a}\right)}{\sqrt{b}+\sqrt{a}+\sqrt{ab}}\)

= \(\dfrac{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)+\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{b}+\sqrt{a}+\sqrt{ab}}\)

= \(\dfrac{\left(\sqrt{a}+\sqrt{b}+\sqrt{ab}\right)\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{b}+\sqrt{a}+\sqrt{ab}}\) = \(\sqrt{a}-\sqrt{b}\)