Question

chứng minh đẳng thức :

với a,b trái dấu \(\dfrac{b-a}{b\cdot\sqrt{\dfrac{-a}{b}}}=\dfrac{a-b}{a\cdot\sqrt{\dfrac{-b}{a}}}\)

Answer 1

\(\text{Với }a< 0;b>0\Rightarrow\dfrac{b-a}{b\sqrt{-\dfrac{a}{b}}}=\dfrac{b-a}{\sqrt{-ab}}\\ \dfrac{a-b}{a\sqrt{-\dfrac{b}{a}}}=\dfrac{a-b}{-\sqrt{-ab}}=\dfrac{b-a}{\sqrt{-ab}}\\ \Rightarrow\dfrac{b-a}{b\sqrt{-\dfrac{a}{b}}}=\dfrac{a-b}{a\sqrt{-\dfrac{b}{a}}}\)

\(\text{Với }a>0;b< 0\Rightarrow\dfrac{b-a}{b\sqrt{-\dfrac{a}{b}}}=\dfrac{b-a}{-\sqrt{-ab}}=\dfrac{a-b}{\sqrt{-ab}}\\ \\ \dfrac{a-b}{a\sqrt{-\dfrac{b}{a}}}=\dfrac{a-b}{\sqrt{-ab}}\\ \Rightarrow\dfrac{b-a}{b\sqrt{-\dfrac{a}{b}}}=\dfrac{a-b}{a\sqrt{-\dfrac{b}{a}}}\)

Vậy.............

Answer 2

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