let a,b,c,d,be positive rationals such that a + sqrt(b) = c + sqrt(d), then either a = c and b = d or b and d are squares of rationals.I found answer here https://www.askiitians.com/forums/10-grade-maths/let-a-b-c-d-be-positive-rationals-such-that-a-b-c_195695.htm but can we not write simply like this:a + sqrt(b) = c + sqrt(d)a = c + sqrt (d) – sqrt (b)as given a is rational hence sqrt (d) and sqrt (b) are rationals. As for RHS to be rational both sqrt has to be rationals i.e d and b are perfect squares.
let a,b,c,d,be positive rationals such that a + sqrt(b) = c + sqrt(d), then either a = c and b = d or b and d are squares of rationals.
I found answer here https://www.askiitians.com/forums/10-grade-maths/let-a-b-c-d-be-positive-rationals-such-that-a-b-c_195695.htm
but can we not write simply like this:
a + sqrt(b) = c + sqrt(d)
a = c + sqrt (d) – sqrt (b)
as given a is rational hence sqrt (d) and sqrt (b) are rationals. As for RHS to be rational both sqrt has to be rationals i.e d and b are perfect squares.
Mudassar Sayyed , 6 Years ago
Grade 12th pass
