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PROVE STEP BY STEP (1)/(2+√(3) ) +(2)/(√(5)-√(3) )+(1)/(2-√(5) ) } = 0<img src="-f-.jpg" alt>
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3 votes
PROVE STEP BY STEP
(1)/(2+√(3) ) +(2)/(√(5)-√(3) )+(1)/(2-√(5) ) } = 0


User Tal Rofe
by
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2 Answers

3 votes

Answer:

Explanation:


(1)/(2+√(3))=(1*(2-√(3)))/((2+√(3))*(2-√(3)))\\\\=(2-√(3))/((2)^(2)-(√(3))^(2))=(2-√(3))/(4-3)\\\\=(2-√(3))/(1)=2-√(3)\\\\(2)/(√(5)-√(3))=(2*(√(5)+√(3)))/((√(5)-√(3))*(√(5) +√(3)))\\\\=(2*(√(5)+√(3)))/((√(5))^(2)-(√(3))^(2))=(2*(√(5)+√(3)))/(5-3)\\\\=(2*(√(5)+√(3)))/(2)=√(5)+√(3)\\\\


(1)/(2-√(5))=(1*(2+√(5)))/((2-√(5))*(2+√(5)))\\\\=(2+√(5))/((2)^(2)-(√(5))^(2))\\\\=(2+√(5))/(4-5)=(2+√(5))/(-1)\\\\= -2-√(5)\\\\\\\\(1)/(2+√(3))+(2)/(√(5)-√(3))+(1)/(2-√(5))=2-√(3)+√(5)+√(3)-2-√(5)=0

User Sjoerd Van Kreel
by
6.3k points
3 votes

Answer:

look at the photo below for the details.

:)

PROVE STEP BY STEP (1)/(2+√(3) ) +(2)/(√(5)-√(3) )+(1)/(2-√(5) ) } = 0<img src-example-1
User Raoof Naushad
by
6.6k points
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