(sqrt(5+)sqrt(3))/(sqrt(3+)sqrt(3+)sqrt(5)) - (sqrt(5-)sqrt(3))/(sqrt(3+)sqrt)とは何ですか(3-)sqrt(5))
2/7 A =(sqrt5 + sqrt3)/(sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3)/(sqrt3 + sqrt3-sqrt5)=(sqrt5 + sqrt3)/(2sqrt3) - (sqrt5) -sqrt3)/(2sqrt3-sqrt5)=(sqrt5 + sqrt3)/(2sqrt3 + sqrt5) - (sqrt5-sqrt3)/(2sqrt3-sqrt5)=((sqrt5 + sqrt3)(2sqrt3-sqrt5) - (sqrt5-sqrt3 )(2sqrt 3 sqrt 5))/((2sqrt 3 sqrt 5) ((2sqrt 15 5 2 * 3 sqrt 15) - (2sqrt 15 5 2 * 3 sqrt 15))/((2sqrt 3)) ^ 2-(sqrt5)^ 2)=(キャンセル(2sqrt15)-5 + 2 * 3キャンセル(-sqrt15) - キャンセル(2sqrt15)-5 + 2 * 3 +キャンセル(sqrt15))/(12-5)=( -10 + 12)/ 7 = 2/7分母が(sqrt3 + sqrt(3 + sqrt5))および(sqrt3 + sqrt(3-sqrt5))の場合、答えは変わります。
(1 / sqrt(a-1)+ sqrt(a + 1))/(1 / sqrt(a + 1)-1 / sqrt(a-1))div sqrt(a + 1)/( (a 1)sqrt(a 1) - (a 1)sqrt(a 1))、a 1?
巨大な数学フォーマット...>色(青)(((1 / sqrt(a-1)+ sqrt(a + 1))/(1 / sqrt(a + 1)-1 / sqrt(a-1)) )/(sqrt(a 1)/((a 1)sqrt(a 1) - (a 1)sqrt(a 1))) 色(赤)(((1 / sqrt(a )) 1)+ sqrt(a + 1))/((sqrt(a-1) - sqrt(a + 1))/(sqrt(a + 1)cdot sqrt(a-1))))/(sqrt(a) + 1)/(sqrt(a-1)cdot sqrt(a-1)cdot sqrt(a + 1) - sqrt(a + 1)cdot sqrt(a + 1)sqrt(a-1))= color(青)(((1 / sqrt(a-1)+ sqrt(a + 1))/((sqrt(a-1)-sqrt(a + 1))/(sqrt(a + 1))cdot sqrt(a -1))))/(sqrt(a + 1)/(sqrt(a + 1))cdot sqrt(a-1)(sqrt(a-1)-sqrt(a + 1)))=色(赤) (((1 / sqrt(a-1)+ sqrt(a + 1))/((sqrt(a-1) - qrt(a + 1))/(sqrt(a + 1))cdot sqrt(a-1) )xx(sqrt(a + 1)cdot sqrt(a-1)(sqrt(a-1) - sqrt(a +
式を単純化しますか?1 /(sqrt(144)+ sqrt(145))+ 1 /(sqrt(145)+ sqrt(146))+ ... + 1 /(sqrt(168)+ sqrt(169))
1最初に注意してください:1 /(sqrt(n + 1)+ sqrt(n))=(sqrt(n + 1) - sqrt(n))/((sqrt(n + 1)+ sqrt(n))( sqrt(n + 1) - sqrt(n))色(白)(1 /(sqrt(n + 1)+ sqrt(n)))=(sqrt(n + 1) - sqrt(n))/(( n + 1) - n)色(白)(1 /(sqrt(n + 1)+ sqrt(n)))= sqrt(n + 1) - sqrt(n)したがって、1 /(sqrt(144)+ sqrt(145)+ 1 /(sqrt(145)+ sqrt(146))+ ... + 1 /(sqrt(168)+ sqrt(169))=(sqrt(145) - sqrt(144))+ (sqrt(146) - sqrt(145))+ ... +(sqrt(169) - qrt(168))= sqrt(169) - sqrt(144)= 13-12 = 1