23check this http://en.wikipedia.org/wiki/Fermat's_Last_Theorem
(1) Find (+ve) integral solution of the equation3x^{2}-2xy+7y^{2}=0
(2) find Integral solution of the equation x^{3}+11^{3}=y^{3}
in 1st quadrant
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6 Answers
23ok (0,11) isnt in first quadrant right ???
yup der will be no solution
see the reason is , Fermat's last theorem
according to this theorem ,
no 3 integers a,b,c where each > 0 ,
can satisfy the eqn an+bn=cn
for n >2
And i guess this question has been asked on this theorem only
1708actually this question is from FIIT-JEE QUIZ......
here we use
x^{3}-y^{3}=-1331 and the factorise
(x-y)(x^{2}+xy+y^{2})=-1331
here both x and y are Integer so
(x-y) and (x^{2}+xy+y^{2}) both are integer
1708thanks for 2 one....
in Question (1) I got no solution but ans=1 solution.