Question

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

Answer 1

Step-by-step explanation:

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

= (3 + √8) / (3)^2 - (√8)^2

= (3 + √8)

1/(√8-√7) = 1/(√8-√7) * (√8+√7)/(√8+√7)

= (√8+√7) / (√8)^2 - (√7)^2

= (√8 + √7)

similarly,

1/(√7 - √6) = (√7 + √6)

1/(√6 - √5) = (√6 + √5)

1/(√7 - 6) = (√7 + 6)

Now,

===) (3 + √8) - (√8 + √7) - (√7 + √6) - (√6 + √5) + (√7 + 6) = 5

===) 3 + √8 - √8 - √7 - √7 - √6 - √6 - √5 + √7 + 6 = 5

===) 3 + 6 = 5

===) 9 = 5

So, the equation is not equal to 5.

I hope, it will help you .