Question

prove that 1 divided by 3 minus root 8 minus 1 / root 8 minus root 7 + 1 divided by root 7 minus root 6 minus 1 divided by root 6 minus root 5 + 1 divided by root 5 minus 2 equals 5​​







IF YOU ANSWER I WILL MARK YOU AS BRAINLIST​

Answer 1

Answer:

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Step-by-step explanation:

Lets first consider LHS, we get:

         1/(3-√8) - 1/(√8 - √7) + 1/(√7 -√6) - 1/(√ 6 - √5) + 1/(√ 5 -2)

Lets rationalise all the denominators, we get:

         1 x (3+√8) / (3-√8) x (3+√8)  - 1 x (√8 + √7) / (√8 - √7) x (√8 +√7)    

+ 1 x (√7 +√6) / (√7 -√6) x (√7 +√6)  -  1 x (√ 6 + √5) / (√ 6 - √5) x (√ 6 + √5)

+ 1 x (√ 5 +2) / (√ 5 -2) x (√ 5 +2)

So after rationalising, we get:

          (3+√8) / 9-8 - { (√8 + √7)/ 8-7 } + (√7 +√6) / 7-6 - { (√ 6 + √5) / 6-5 } + (√5 +2) / 5-4

Now solving with denominator as 1, we get:

          3+√8- √8 - √7 +√7 +√6 -√ 6 - √5 + √5 +2

Cancelling the root terms, we get the final answer as:

         5

         = RHS.

Answer:

       So from above solution we have proved that :

       1/(3-√8) - 1/(√8 - √7) + 1/(√7 -√6) - 1/(√ 6 - √5) + 1/(√ 5 -2) = 5

Answer 2

Answer:

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