Question

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

Answer 1

Answer: 1

Step-by-step explanation:

for a*b to be equal to one, a has to be 1/b, therefore a=1/b, so we already know the equation will be aˆ3/aˆ3. Through some simple algebra, you can understand that aˆ3 +bˆ3 is also = to 1

just to make sure:

aˆ3 = (5 + 2√6) * (5 + 2√6) * (5 + 2√6)

bˆ3 = 1 / ((5 + 2√6) * (5 + 2√6) * (5 + 2√6))

aˆ3 = (25+20√6+24) (5+2√6) = (49 +20√6) (5+2√6)

= 245+98√6+100√6+240

aˆ3 = 485 + 198√6

therefore, bˆ3 = (1) / (485 + 198√6)

$\frac{(485 +198\sqrt{6} )}{(485 +198\sqrt{6} )}$

and through simple algebra, aˆ3+bˆ3 = 1