Question

prove that 1by √4+√5+1by√5+√6+1by√6+√7+1by√7+√8+1by√8+√9=1​

Answer 1

Answer:

1 / (√4 + √5) = [1 / (√4 + √5)] x [(√4 - √5)/(√4 - √5)] = (√4 - √5) / (√4)2 - (√5)2 = (√4 - √5) / 4 - 5 = (√4 - √5) / (-1) = (√5 - √4) (1 / √5 + √6) = [1 / (√5 + √6)] x [(√5 - √6)/(√5 - √6)] = (√5 - √6) / (√5)2 - (√6)2 = (√5 - √6) / 5 - 6 = (√5 - √6) / (-1) = (√6 - √5) Similarly, (1 / √6 + √7) = (√7 - √6) (1 / √7 + √8) = (√8 - √7) (1 / √8 + √9) = (√9 - √8) (1 / √4 + √5) + (1 / √5 + √6) + (1 / √6 + √7) + (1 / √7 + √8) + (1 / √8 + √9) = (√5 - √4) + (√6 - √5) + (√7 - √6) + (√8 - √7) + (√9 - √8) = 3 - 2 = 1