Question

divide 56 in 2 parts in ap such that the ratio of the product of their extremes to the product of means 5:6.​

Answer 1

Answer:

Given:

↬ 56 is divided into four parts which form an A.P.

↬ Ratio of the product of extremes of given A.P. to the product of their means is 5:6

To Find:

All the parts of 56

Things to know before solving question

(a+b)(a-b)= a² -b²

Solution:

Let the four parts be a-3d, a-d, a+d, a+3d such that they are in A.P.

Now,

Sum of all parts= 56

⇒ a-3d+a-d+a+d+a+3d= 56

⇒ 4a= 56

⇒ a= 14

On putting value of a in above equation, we get

Now,

Case-1 ,when d=2

First part= a-3d= 14-3(2)= 8

Second part= a-d= 14-2= 12

Third part= a+d= 14+2= 16

Fourth part= a+3d= 14+3(2)= 20

Case-2 ,when d= -2

First part= a-3d= 14-3(-2)= 20

Second part= a-d= 14-(-2)= 16

Third part= a+d= 14+(-2)= 12

Fourth part= a+3d= 14+3(-2)= 8

Hence, all four parts are 8, 12, 16 and 20.

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