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in Arithmetic Progression by (29.9k points)
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The sum of three numbers in AP is 3 and their product is -35. Find the numbers.

1 Answer

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Best answer

Let the required numbers be (a - d), a and (a + d).

Then (a - d) + a + (a + d) = 3

\(\Rightarrow\) 3a = 3

\(\Rightarrow\) a = 1

Also, (a - d).a.(a + d) = -35

\(\Rightarrow\) a(a2 - d2) = -35

\(\Rightarrow\) 1.(1 - d2) = -35

\(\Rightarrow\) d2 = 36

\(\Rightarrow\) d = \(\pm6\)

Thus, a = 1 and d = \(\pm6\)

Hence, the required numbers are (-5,1 and 7) or (7,1 and -5).

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