Question

Please help with the following question:

Find rational numbers a and b such that:

(7+5√2) ^ 1/3 = a+b√2
Thank you

Answer 1

my first thoughts would be to cube both sides to eliminate the 1/3 exponent

Answer 2

have u tried that ?

Answer 3

yes

Answer 4

so, in which step are you stuck ?

Answer 5

i get a multiple of complex equations

Answer 6

did u get
a(a^2+6b^2) =7

and
b(2b^2+3a^2) =5

bdw, that ^ clearly suggests a=1,b=1 as one solution

Answer 7

yes i got that

Answer 8

you can just stop that
because thats the only real solution!

Answer 9

stop there***

Answer 10

oh, and since you are new here,
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Answer 11

thanks