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Class 10 > Learn Mathematics > Three numbers are in A.P. If the sum of these numbers...
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Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers?

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Let the 3 terms are (a - b), a, and (a + b). So, (a - b) + a + ( a + b) = 27=> 3a=27 => a=9. Now the product is 648. So, (9 - b) x 9 x (9 + b) = 648=> (81 - b^2) = 648/9 = 72=> b^2 = 81 - 72=9 => b = =3 or b = -3. For, b = 3, the numbers are: (9 - 3), 9, (9 + 3) = 6, 9, 12 or (9 - (-3)), 9...
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Let the 3 terms are (a - b), a, and (a + b). So, (a - b) + a + ( a + b) = 27=> 3a=27 => a=9. Now the product is 648. So, (9 - b) x 9 x (9 + b) = 648=> (81 - b^2) = 648/9 = 72=> b^2 = 81 - 72=9 => b = =3 or b = -3. For, b = 3, the numbers are: (9 - 3), 9, (9 + 3) = 6, 9, 12 or (9 - (-3)), 9 , (9 + (-3)) = 12, 9, 6 The three numbers are 6, 9, 12 or 12, 9, 6 (Answer) read less
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