Question

Tính giá trị của biểu thức

K=\(\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+...+\dfrac{5}{45\cdot46}\)

H=3,5:x-0,4xy+y:x với |x|=0,5; y=1,5

T=0,2\(\sqrt{6x}-\dfrac{3}{2}\sqrt{xy}+0,5\sqrt{6y}\) với x= \(\dfrac{2}{3}\) và y=\(\dfrac{8}{75}\)

Answer 1

\(K=5\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{45\cdot46}\right)\)

\(=5\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{45}-\dfrac{1}{46}\right)\)

=5*45/46=225/46

\(T=\dfrac{1}{5}\cdot\sqrt{6\cdot\dfrac{2}{3}}-\dfrac{3}{2}\cdot\sqrt{\dfrac{2}{3}\cdot\dfrac{8}{75}}+\dfrac{1}{2}\cdot\sqrt{6\cdot\dfrac{8}{75}}\)

\(=\dfrac{1}{5}\cdot2-\dfrac{3}{2}\cdot\dfrac{4}{15}+\dfrac{1}{2}\cdot\dfrac{4}{5}\)

=2/5-12/30+4/10

=2/5