Question

find positive integers a,b such that :
(\sqrt[3]{a}+\sqrt[3]{b}-1)^{^{2}}=49 + 20 \sqrt[3]6{}

Answer 1

edit the question plz...

Answer 2

\(\large (\sqrt[3]{a}+\sqrt[3]{b}-1)^{^{2}}=49 + 20 \sqrt[3]6{}\) ?

Answer 3

yes, that is right :d

Answer 4

well how about the question itself?

finding all pairs of (a,b) or just one pair

Answer 5

find all pairs :d

Answer 6

lol.....very hard problem...

Answer 7

yes...

Answer 8

\[49+20\sqrt [3]{6}= (\sqrt [3]{48}+\sqrt [3]{288}-1)^{2}\]
so
\[(\sqrt [3]{a}+\sqrt [3]{b}-1)^{2}= (\sqrt [3]{48}+\sqrt [3]{288}-1)^{2}\] and
\[\sqrt [3]{a}+\sqrt [3]{b}=\sqrt [3]{48}+\sqrt [3]{288}\]

Answer 9

but having other pairs (a,b) ?

Answer 10

i have to think again....but i guess there is one pair...(a,b)=(48,288)

Answer 11

yes :d