Sequences and series -2
If [ b − c ] x 2 + [ c − a ] x y + [ a − b ] y 2 is a perfect square,then a,b,c are in
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1 solution
Your whole question omitted a lot of necessary details. If x = y = 0 , then the expression is a perfect square and a , b , c can be anything you want, not only in A.P. You'll have to add the domains of a , b , c , x , y .
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it is not necessary
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you might have meant " ∀ x , y " then. Either way, you'll have to add something to the problem. The domains should be shown as well.
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@Mathh Mathh – actually it is IITJEE question and and question was this much only
You must mention in your solution that it is a quadratic in y x or x y .
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It doesn't matter, their is analogy and thus it is same in either of cases.
could anyone tell me what those 3 dots to the left of the 1st expression mean?
It is a quadratic eq. therefore discriminant=0 for a perfect square. ∴ [ c − a ] 2 − 4 [ b − c ] [ a − b ] = 0 [ c + a ] 2 − 4 b [ c + a ] + 4 b 2 = 0 [ c + a − 2 b ] 2 = 0 c + a = 2 b . We got the relation of A.P