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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.
 
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.

Grade:12th pass

1 Answers

Arun
25757 Points
3 years ago
Dear student
 
a + sqrt (b) means b is in shortest form and not a perfect square.
 
Hope it helps
 
Regards
Arun (askIITians forum expert)

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