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

2
by sidharthb2000

2014-09-04T20:14:19+05:30

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=1/(3-2.828)-1/(2.828-2.645)+1/(2.645-2.449)-1/(2.449-2.236)+1/(2.236-2)
=1/(0.172)-1/(0.183)+1/(0.916)-1/(0.213)+1/(0.236)
=5.813-5-4644+5.1020-4.6948+4.237
=4.99
=5      Approximately
2014-09-04T21:47:09+05:30

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1/(3-√8) - 1/(√8-√7) + 1/(√7-√6) - 1/(√6-√5) + 1/(√5-2) = 51/(3-rt8)=[1/(3-rt8)]{(3+rt8)/(3+rt8)]  ..... (by rationalising)
=(3+rt8)/(9-8)       from ...a^2-b@=(a+b)(a-b)
=3+rt8
as first term all terms will be rationalised...so the expression becomes
3+rt8-rt8-rt7+rt7+rt6-rt6-rt5+rt5+2
then all root terms will get cancelled
=3+2=5