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Algebra

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 Joined: 3 Jun 2012 Post: 21
3 Jun 2012 14:17:05 IST
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Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

If a,b,c and d are positive integers and a<b<c<d  such that a,b,c are in A.P. and b,c,d are in G.P. and d-a=30.Find the four numbers.

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Joined: 18 Feb 2012
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5 Jun 2012 08:48:04 IST
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-3,3,9,27(b,c and d are positive integers)

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7 Jun 2012 13:40:06 IST
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9 Jun 2012 16:58:56 IST
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Let a = a then b = (a+c)/2 c = sqrt((a+c)*(a+30)/2)  and d = 30

Take c = sqrt((a+c)*(a+30)/2). Make a quadratic equation and find its discriminant. Think of a such that D is perfect square. Only then we can get integral solution. From this approach I got a = 18 b = 27 c = 36 and d = 48 as the answer.

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