Question

СРОЧНО,60Б
УПРОСТИТЕ ВЫРАЖЕНИЕ (3√10+1)*(√5/√8+√5 - √2/√5-√8)

Answer 1

$(3sqrt{10}+1)( frac{sqrt5}{sqrt8+sqrt5}-frac{sqrt2}{sqrt5-sqrt8})=\\=(3sqrt{10}+1)cdot frac{5-sqrt{40}-sqrt{16}-sqrt{10}}{(sqrt5-sqrt8)(sqrt5+sqrt8)} =\\=(3sqrt{10}+1)cdot frac{5-2sqrt{10}-4-sqrt{10}}{5-8} =(1+3sqrt{10})cdot frac{1-3sqrt{10}}{-3} =\\= frac{1^2-(3sqrt{10})^2}{-3} =-frac{1-9cdot 10}{3} =- frac{-89}{3} = frac{89}{3} =29frac{2}{3}$