Question

if a = 5 + 2√6 and ab = 1, find a3 + b3​

Answer 1

Answer!!

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