Question

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

Answer 1

Proof:

`(1)/(0.17157287525 ) -(1)/(0.18267581368) +(1)/(0.19626156828) -(1)/(0.21342176528) +(1)/(0.2360679775)`

`5.82842712475-5.47417843581+5.09524105385-4.68555772028`

`+4.2360679775`

`=5.00000000001`

Answer 2

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

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

- (√6+√5)/(√6+√5)(√6-√5) + (√5+2)/(√5+2)(√5-2)=

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

= 3 + 2 = 5

proved