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Question

If a=5+25-2 and b=5-25+2, show that 3a2+4ab-3b2=4+56310.

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Solution

According to question,
a=5+25-2 and b=5-25+2

a=5+25-2 =5+25-2×5+25+2 =5+2252-22 =52+22+2525-2 =5+2+2103 =7+2103 ...1b=5-25+2 =5-25+2×5-25-2 =5-2252-22 =52+22-2525-2 =5+2-2103 =7-2103 ...2
Now,
3a2+4ab-3b2=3a2-b2+4ab=3a+ba-b+4ab=37+2103+7-21037+2103-7-2103+47+2103×7-2103=31434103+472-21029=56310+449-409=56310+4
Hence, 3a2+4ab-3b2=4+56103.

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