Question: Divide 45 into three parts which are in AS such that their product is 1875.

Solution:

Let the three numbers which are in AS be (a-d), a and (a +d).

According to the question,
or, a-d + a + a +d = 45

or, 3a = 45

or, a = \frac{45}{3}

\therefore a = 15


Also,
(a -d)(a)(a +d) = 1875

or, a (a² - d²) = 1875

or, 15(15^2 - d^2) = 1875

or, 225 - d^2 = \frac{1875}{15}

or, 225 - d^2 = 125

or, d^2 = 225 - 125

or, d^2 = 100

or, d = \sqrt{100}

\therefore d = \pm 10


When d = +10,
(a - d) = (15-10) = 5
a = 15
(a + d) = (15+10) = 25

When d = -10,
(a -d) = (15+10) = 25
a = 15
or, (a + d) = (15-10) = 5


Hence, the three parts in which 45 was divided are either 5,15,25 or 25,15,5.

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