Question

4 number are in A.S the sum of the first and fourth is 14 and the product of the second and third is 45 find the number

Answer 1

$let \: \: the \: \: numbers \: \: be \\ a - 3d \: \: \: a - d \: \: \: a + d \: \: \: a + 3d \\ given \\ (a - 3d) + (a + 3d) = 14 \\ 2a = 14 \\ a = 7 \\ given \\ (a - d) \times (a + d) = 45 \\ {a}^{2} - {d}^{2} = 45 \\ {7}^{2} - {d}^{2} = 45 \\ d = + \: \: or \: \: - 2$
Therefore the sequence of numbers are
1, 5, 9, 13 for d=2
And
13, 9, 5, 1 for d=-2