if a = 5 + 2√6 and ab = 1, find a3 + b3
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a=5+2√6, b=1/a=1/(5+2√6)
a²+b²=a²+1/a²
=(5+2√6)²+1/(5+2√6)²
=(25+24+10√2)+1(5-2√6)²/(5+2√6)²(5-2√6)²
=(49+10√2)+(5-2√6)²/(5²-2√6²)
=(49+10√2)+(25+24-10√2)/(25-24)
=(49+10√2)+(49-10√2)/1
=49+10√2+49-10√2
=98
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