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a=a equals square root of 3 minus square root of 2 divided by square root of 3 plus square root of 2 space a n d space b equals space square root of 3 plus square root of 2 divided by square root of 3 minus square root of 2 space comma t h e n space f i n d space a to the power of 2 space end exponent plus space b squared

Asked by smra129 11th September 2015, 8:03 AM
Answered by Expert
Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n s comma a equals fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 plus square root of 2 end fraction space a n d space b equals fraction numerator square root of 3 plus square root of 2 over denominator square root of 3 minus square root of 2 end fraction therefore a squared plus b squared equals open parentheses fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 plus square root of 2 end fraction close parentheses squared plus open parentheses fraction numerator square root of 3 plus square root of 2 over denominator square root of 3 minus square root of 2 end fraction close parentheses squared space space space space space space space space space space space space space equals open parentheses square root of 3 minus square root of 2 close parentheses squared over open parentheses square root of 3 plus square root of 2 close parentheses squared plus open parentheses square root of 3 plus square root of 2 close parentheses squared over open parentheses square root of 3 minus square root of 2 close parentheses squared space space space space space space space space space space space space space equals fraction numerator open parentheses square root of 3 minus square root of 2 close parentheses to the power of 4 plus open parentheses square root of 3 plus square root of 2 close parentheses to the power of 4 over denominator open parentheses square root of 3 plus square root of 2 close parentheses squared open parentheses square root of 3 minus square root of 2 close parentheses squared end fraction space space space space space space space space space space space space space equals fraction numerator open square brackets open parentheses square root of 3 minus square root of 2 close parentheses squared close square brackets squared plus open square brackets open parentheses square root of 3 plus square root of 2 close parentheses squared close square brackets squared over denominator open parentheses square root of 3 plus square root of 2 close parentheses squared open parentheses square root of 3 minus square root of 2 close parentheses squared end fraction space space space space space space space space space space space space space equals fraction numerator open parentheses 3 plus 2 minus 2 square root of 6 close parentheses squared plus open parentheses 3 plus 2 plus 2 square root of 6 close parentheses squared over denominator open square brackets open parentheses square root of 3 plus square root of 2 close parentheses open parentheses square root of 3 minus square root of 2 close parentheses close square brackets squared end fraction space space space space space space space space space space space space space equals fraction numerator open parentheses 5 minus 2 square root of 6 close parentheses squared plus open parentheses 5 plus 2 square root of 6 close parentheses squared over denominator open square brackets 3 minus 2 close square brackets squared end fraction space space space space space space space space space space space space space equals open parentheses 25 plus 24 minus 20 square root of 6 close parentheses plus open parentheses 25 plus 24 plus 20 square root of 6 close parentheses space space space space space space space space space space space space space equals 25 plus 24 plus 25 plus 24 space space space space space space space space space space space space space equals 98

Answered by Expert 11th September 2015, 11:48 AM
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