Question

giúp mik nha

Answer 1

\(D=\dfrac{1}{2a-1}\cdot\sqrt{25a^4-100a^5+100a^6}\)

\(=\dfrac{1}{2a-1}\cdot\sqrt{\left(5a^2-10a^3\right)^2}\)

\(=\dfrac{1}{2a-1}\cdot\left(5a^2-10a^3\right)\)

\(=\dfrac{5a^2-10a^3}{2a-1}\)

Answer 2

D = \(\dfrac{1}{2a-1}\sqrt{25a^4-100a^5+100a^6}\) = \(\dfrac{1}{2a-1}\sqrt{a^4\left(25-100a+100a^2\right)}\)

D = \(\dfrac{1}{2a-1}\sqrt{a^4\left(10a-5\right)^2}\) (1)

th1: \(x< \dfrac{1}{2}\) thì D \(\Leftrightarrow\) \(\dfrac{a^2\left(5-10a\right)}{2a-1}\) = \(\dfrac{-5a^2\left(2a-1\right)}{2a-1}\) = \(-5a^2\)

th2 : \(x>\dfrac{1}{2}\) thì D \(\Leftrightarrow\) \(\dfrac{a^2\left(10a-5\right)}{2a-1}\) = \(\dfrac{5a^2\left(2a-1\right)}{2a-1}\) = \(5a^2\)

vậy D = \(\pm5a^2\)

Answer 3

D = \(\dfrac{1}{2a-1}.\sqrt{25a^4-100a^5+100a^6}\)

D = \(-\dfrac{1}{1-2a}.\sqrt{\left(5a^2-10a^3\right)^2}\)

D = \(-\dfrac{1}{1-2a}.\left(5a^2-10a^3\right)\)

D = \(\dfrac{-\left(5a^2-10a^3\right)}{1-2a}\)

D = \(\dfrac{-5a^2\left(1-2a\right)}{1-2a}=-5a^2\)