Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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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. - Mathematics

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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Solution

\[\text { Let the three numbers be } a - d, a, a + d . \]

\[\text {Their sum } = 27\]

\[ \Rightarrow a - d + a + a + d = 27\]

\[ \Rightarrow 3a = 27\]

\[ \Rightarrow a = 9 . . . (i)\]

\[\text { Product } = (a - d)a(a + d) = 648\]

\[ \Rightarrow a( a^2 - d^2 ) = 648\]

\[ \Rightarrow 9(81 - d^2 ) = 648\]

\[ \Rightarrow (81 - d^2 ) = 72\]

\[ \Rightarrow d^2 = 9\]

\[ \Rightarrow d = \pm 3\]

\[\text { When a = 9, d = 3, we have:} \]

\[6, 9, 12\]

\[\text { When a = 9, d = - 3, we have: } \]

\[12, 9, 6\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.2 | Q 2 | Page 15
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