The sum of three numbers in AP is 3 and their product is -35. Find the

1.	The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
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).

The sum of three numbers in AP is 3 and their product is -35. Find the numbers.

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).