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  • Break 24 into 3 parts that are in A.P, such that product of extreme terms is 4 more than thrice the middle term.    Option:

Break 24 into 3 parts that are in A.P, such that product of extreme terms is 4 more than thrice the middle term.


 

 

Option: 1

2,8,14


Option: 2

5,10,11


Option: 3

8,8,8


Option: 4

None of these


Answers (1)

best_answer

Let 3 parts be  a - d, a, a + d

As their sum = 24

\Rightarrow a-d+a+a+d=24

\Rightarrow 3a=24

\Rightarrow a=8

So terms are 8-d, 8, 8+d

Also given (8-d)(8+d)=3\times 8+4

\Rightarrow 64-d^2=28

\Rightarrow d^2=36

\Rightarrow d=6 \; \; \text{or}\; -6

So terms are 2, 8, 14 (for d = 6) or

                      14, 8, 2 (for d = -6)

Posted by

Devendra Khairwa

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