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If a = 2+√3 , then find the value of a-1/a

July 28, 2018 0
a equals 2 plus square root of 3 a minus 1 over a equals 2 plus square root of 3 minus fraction numerator 1 over denominator 2 plus square root of 3 end fraction equals 2 plus square root of 3 minus left parenthesis fraction numerator 1 over denominator 2 plus square root of 3 end fraction cross times 1 right parenthesis equals 2 plus square root of 3 minus left parenthesis fraction numerator 1 over denominator 2 plus square root of 3 end fraction cross times fraction numerator 2 minus square root of 3 over denominator 2 minus square root of 3 end fraction right parenthesis space space space space space space space space left square bracket fraction numerator 2 minus square root of 3 over denominator 2 minus square root of 3 end fraction equals 1 right square bracket equals 2 plus square root of 3 minus left parenthesis fraction numerator 2 minus square root of 3 over denominator 2 squared minus left parenthesis square root of 3 right parenthesis squared end fraction right parenthesis space space space space space space left square bracket u s e space left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis equals a squared minus b squared right square bracket equals 2 plus square root of 3 minus fraction numerator 2 minus square root of 3 over denominator 4 minus 3 end fraction equals 2 plus square root of 3 minus left parenthesis fraction numerator 2 minus square root of 3 over denominator 1 end fraction right parenthesis equals 2 plus square root of 3 minus 2 plus square root of 3 equals 2 square root of 3
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