Question

cho số thực a<1. Rút gọn biểu thức \(P=\sqrt{\frac{15}{2}}\cdot\sqrt{\frac{10\cdot\left(a-1\right)^2}{3}}\)

Answer 1

hay tk dung cho toi

Answer 2

\(P=\sqrt{\frac{15}{2}}.\sqrt{\frac{10.\left(a-1\right)^2}{3}}\)    ( ĐK a<1 )

\(\Leftrightarrow P=\frac{\sqrt{15}}{\sqrt{2}}.\frac{\sqrt{10}.\sqrt{\left(a-1\right)^2}}{\sqrt{3}}\)

\(\Leftrightarrow P=\frac{\sqrt{15}.\sqrt{2}}{2}.\frac{\sqrt{10}.\sqrt{3}.\left|a-1\right|}{3}\)

\(\Leftrightarrow P=\frac{\sqrt{30}}{2}.\frac{\sqrt{30}\left(1-a\right)}{3}\)( vì a-1<0)

\(\Leftrightarrow P=\frac{\sqrt{30}.\sqrt{30}\left(1-a\right)}{2.3}\)

\(\Leftrightarrow\frac{30\left(1-a\right)}{6}\)

\(\Leftrightarrow5\left(1-a\right)\)