Question

化简：(-√2+√3+√5)(√2-√3+√5)(√2+√3-√5)(√2+√3+√5)

Answer 1

(-√2+√3+√5)(√2-√3+√5)(√2+√3-√5)(√2+√3+√5)
=【（√5）²-（√2-√3)²】【(√2+√3）²-（√5)²】
=【5-5+2√6】【5+2√6-5】
=2√6×2√6
=24

Answer 2

解：

原式=[√5 -(√2 -√3)][√5 +(√2 -√3)]×[(√2 +√3)-√5][(√2 +√3)+√5]
=[(√5)^2 -(√2 -√3)^2]×[(√2 +√3)^2 -(√5)^2]
=[5-(2+3-2√6)]×[(5+2√6)-5]
=2√6 ×2√6
=24

满意我的回答记得采纳，谢谢

Answer 3

解：
(2√3-2)(3√6+√2)+(3√3+5√2)/(3√3-5√2)
=2(√3-1)*√2(3√3+1)+[(3√3+5√2)(3√3+5√2)]/[(3√3-5√2)(3√3+5√2)]
=2√2(9-3√3+√3-1)+(27+50+30√6)/(27-50)
=2√2(8-2√3)-(77+30√6)/23
=16√2-4√6-77/23-30√6/23
=16√2-122√6/23-77/23