Question

Вычислите значение выражения ((2.5^((3)/(4) )-1)/(2.5^((1)/(4))-1)+2.5^((1)/(4)))^((1)/(2))((2.5^((3)/(4) )+1)/(2.5^((1)/(4))+1)-2.5^((1)/(2)))*(2.5-2.5^((3)/(2)))^(-1)

Answer 1

$(\frac{2,5^{\frac{3}{4}}-1}{2,5^{\frac{1}{4}}-1} +2,5^{\frac{1}{4}})^{\frac{1}{2}}*(\frac{2,5^{\frac{3}{4}}+1}{2,5^{\frac{1}{4}}+1} +2,5^{\frac{1}{2}})*(2,5-2,5^{\frac{3}{2} })=0,4$

$1) (\frac{2,5^{\frac{3}{4}}-1}{2,5^{\frac{1}{4}}-1} +2,5^{\frac{1}{4}})^{\frac{1}{2}}=(\frac{(2,5^{\frac{1}{4}}-1)(2,5^{\frac{1}{2}}+2,5^{\frac{1}{4}}+1)}{2,5^{\frac{1}{4}}-1} +2,5^{\frac{1}{4}})^{\frac{1}{2}}=(2,5^{\frac{1}{2}}+2,5^{\frac{1}{4}}+1 +2,5^{\frac{1}{4}})^{\frac{1}{2}}=(2,5^{\frac{1}{2}}+2*2,5^{\frac{1}{4}}+1)^{\frac{1}{2}}=((2,5^{\frac{1}{4}}+1)^2)^{\frac{1}{2}}=2,5^{\frac{1}{4}}+1$

$2) (\frac{2,5^{\frac{3}{4}}+1}{2,5^{\frac{1}{4}}+1} -2,5^{\frac{1}{2}})=\frac{(2,5^{\frac{1}{4}}+1)(2,5^{\frac{1}{2}}-2,5^{\frac{1}{4}}+1)}{2,5^{\frac{1}{4}}+1} +2,5^{\frac{1}{2}}=2,5^{\frac{1}{2}}-2,5^{\frac{1}{4}}+1 -2,5^{\frac{1}{2}}=1-2,5^{\frac{1}{4}}$

$3) \frac{(1-2,5^{\frac{1}{4}})(2,5^{\frac{1}{4}}+1)}{2,5-2,5^{\frac{3}{2}})} =\frac{(1-2,5^{\frac{1}{2}})}{2,5(1-2,5^{\frac{1}{2}})} =\frac{1}{2,5} =1:\frac{5}{2}=\frac{2}{5} =0,4$

ответ: 0,4