Question 1036257
.In an A.P, the sum of three positive consecutive numbers is 21. The sum of their squares is 155.Find the numbers
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Let x be the middle term of the AP (the second term) and d be the common difference.

Then the three terms are x-d, x, and x+d, and their sum is 3x = 21 --->  x  = {{{21/3}}} = 7. 

The second condition is 

{{{(7-d)^2 + 7^2 + (7+d)^2}}} = 155,

which gives 

{{{49 - 14d + d^2 + 49 + 49 + 14d + d^2}}} = 155, 

147 + 2d^2 = 155,

2d^2 = 155 - 147 = 8,  --->  d^2 = 4  --->  d = +/-2.

So, the progression is  5, 7, 9  or  9, 7, 5.

<U>Answer</U>. {5, 7, 9}  or  {9, 7, 5}.
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