CBSE Class 11-science Answered
Sir\Madam please explain me this question on Arithmetic Progressions!!
Asked by | 11 Jan, 2010, 02:41: PM
Expert Answer
Let the four integers be, a-3d, a-d, a+d, and a+3d.
Their sum,
a-3d + a-d + a+d + a+3d = 4a = 24,
a = 6
and product,
(a-3d)(a-d)(a+d)(a+3d) =
(a2-9d2)(a2-d2) = 945
(36 - 9d2)(36 - d2) = 945
9(4 - d2)(36 - d2) = 945
(4 - d2)(36 - d2) = 105
d4 - 40d2 + 144 - 105 = 0
d4 - 40d2 + 39 = 0
Solving this quadratic equation in d2
d2 = {40±
(1600-(4x39)}/2
= {40±38}/2
Hence d =1 and the four integers are,
3, 5, 7, 9
Regards,
Team,
TopperLearning.
Answered by | 11 Jan, 2010, 03:02: PM
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