The sum of 3 number of an A.P is 21 and their product is 231 . Find th

1.	The sum of 3 number of an A.P is 21 and their product is 231 . Find the number?
Answer» Let the required numbers be (a-d), a and (a + d).............(1)Then, according to question, (a\xa0- d) + a + (a + d) = 21\xa0{tex}\\Rightarrow{/tex}\xa03a\xa0= 21{tex}\\Rightarrow{/tex}\xa0a=7.And, (a - d){tex} \\cdot {/tex}a{tex} \\cdot {/tex}(a+d) = 231{tex}\\Rightarrow{/tex}a (a2 - d2) = 231{tex}\\Rightarrow{/tex}7(49-d2) = 231 [{tex}\\because {/tex}a=7]{tex}\\Rightarrow{/tex}7d2=343-231=112{tex}\\Rightarrow{/tex}d2=16\xa0{tex}\\Rightarrow{/tex}d={tex} \\pm {/tex}4.Thus, a=7 and d=\xa0{tex} \\pm {/tex}4. Now substitute these values of a and d in above equation (1).Therefore, the required numbers are(3,7,11) or (11,7,3).

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