For any rational x and y prove that x^2+y^2=3

For any rational x and y prove that x^2+y^2=3


3 Answers

sudhir pal
askIITians Faculty 26 Points
9 years ago
this question is wrong
for disapproving lets put x=2 and y = 3 (both are rational) and since expression is true for any rational which is not true
please rewrite the question again
Thanks & Regards
askIITians Faculty
IIT Delhi
Mostafijur Rahaman
40 Points
9 years ago
srry the question will be prove that for any there is no rational x&y such that x^2+y^2 equal to 3.
mycroft holmes
272 Points
9 years ago
Suppose there are rationals satisfying this equation, we have (m/n)^2+(k/l)^2 = 3 or (ml)^2+(kn)^2 = 3(ln)^2 Note that the highest power of 3 that divides LHS is even, while it is odd on RHS. Hence this equation is impossible in integers. Hence no rational solutions exist

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