各位數學高手幫幫忙..

Question

各位數學高手幫幫忙呀..
有幾提數學題目請幫忙解答..謝謝
1/(√3+√2) + 2/(√5+√3) + 3/(√8+√5)
請化解...
請付詳解...
感激不盡...

Answer 1

解題技巧：(分母根式的有理化)[1 / (√a + √b)][(√a - √b) / (√a - √b)] = [(√a - √b) / (√a2 - √b2)]= [(√a - √b) / (a - b)]使用公式：(平方差)(x + y)(x - y) = x2 - y2------------------------------------------[1 / (√3 + √2)][(√3 - √2) / (√3 - √2)] = (√3 - √2)[2 / (√5 + √3)][(√5 - √3) / (√5 - √3)] = (√5 - √3)[3 / (√8 + √5)][(√8 - √5) / (√8 - √5)] = (√8 - √5)1 / (√3 + √2) + 2 / (√5 + √3) + 3 / (√8 + √5)= ( √3 - √2) + ( √5 - √3) + (√8 - √5) [合併同類根式]= (√8 - √2)= 2√2 - √2= √2

Answer 2

=1(√3-√2)/(√3+√2)(√3-√2)+ 2(√5-√3)/(√5+√3)(√5-√3)+ 3(√8-√5) /(√8+√5) (√8-√5)
=(√3-√2)/3-2 + 2√5-2√3/5-3 + 3√8-3√5/8-5
=(√3-√2) + 2√5-2√3/2 + 3√8-3√5/3
=√3-√2 + √5-√3 + √8-√5
= √8-√2
=2√2-√2
=√2

Answer 3

我算了...
可是我回答次數用完了~"~
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