Question

(1/√2-1/√3)*2√6-(1/√3-1/√5)*√15-(-1/√5+1/√2)*√10

Answer 1

(1/√2-1/√3)×2√6-(1/√3-1/√5)×√15-(-1/√5+1/√2)×√10 =

( √2 / 2 - √3 / 3) × 2√6 - ( √3 / 3 - √5 / 5 )×√15 - ( -√5 / 5 + √2 / 2) ×√10 =

=(3√2/ 6 - 2√3 / 6 ) × 2√6 - (5√3 / 15 - 3√5 / 15 ) × √15 - ( - 2√5 / 10 + 5√2/10) ×√10=

= 6√12 / 6 - 4√18/6 - 5√45 / 15 + 3√75 / 15 + 2√50 / 10 - 5√20 / 10 =

= 2√ 3 - 12√2 / 6 - 15√5/ 15 + 15 √3 / 15 + 10√2 / 10 - 10√5 / 10 =

= 2√3 - 2√2 - √5 + √3 + √2 - √5 =

= 3√3 - √2 - 2√5