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Doubt & Answer Explanation

Doubt

"Divide 72 into 4 parts so that they form an AP & also product of least 2 parts is 480" please solve this question with explation.

Answer Explanation

Let the four terms in A.P would be

(a-3d) +(a-d) +(a+d) + (a+3d) = 72

4a=72

(a = 18)

Now , we have given
(a-3d).(a-d)=480

(18-3d)(18-d) =480 (from(i))
324-18d-54d+3d² =480

3d² -72d=480-354
3d² -72d-156=0
d² -24d-52 =0
d² -26d+2d-52 =0
d(d-26) + 2 (d-26) = 0
(d+2) (d.26)=0
d=-2 or 26

We will take d = -2

therefore the no. are a-3d =18-3(2)
=18+6
=24

Similarly a -d = 20
a+d=16&a+3d = 12

& 24,20,16,& 12 are all in A.P

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