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For arithemetic progression addition of three terms is 15 and addition of their squres is 83 , then find that numbers

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Your problem `->` For arithemetic progression addition of three terms is 15 and addition of their squres is 83 , then find that numbers


Let the terms are `a-d, a, a+d`

Addition of this terms is `15`

`=> (a-d) + a + (a+d) = 15`

`=> 3 a = 15`

`=> a = 15/3 = 5`

Addition of their square is `83`

`=> (a-d)^2 + a^2 + (a+d)^2 = 83`

`=> a^2 - 2ad + d^2 + a^2 + a^2 + 2ad + d^2 = 83`

`=> 3a^2 + 2d^2 = 83`

`=> 3(5)^2 + 2d^2 = 83`

`=> 2d^2 = 8`

`=> d^2 = 4`

`=> d = +- 2`

`d = +2 =>` Required terms : `5 - 2, 5, 5 + 2 => 3, 5, 7`

`d = -2 =>` Required terms : `5-(-2), 5, 5-2 => 7, 5, 3`






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