Question

Divide 15 into three parts which are in A.P. and the sum of their squares is 83.

Answer 1

Answer:

the numbers are 3,5,7 or, 7,5,3.

refer to the attachment for the solution.

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Answer 2

Answer:

SUPPOSE THE NUMBERS ARE –

$(a - d) \: ,\: a \:, \: (a + d)$

SUM OF THEM –

$3a = 15$

$a = 5$

SUM OF THEIR SQUARE –

${(5 - d)}^{2} + {5}^{2} + {(5 + d)}^{2} = 83 \\ \\ 25 + {d}^{2} - 10d + 25 + 25 + {d}^{2} + 10d = 83 \\ \\ 2 {d}^{2} + 75 = 83 \\ \\ 2 {d}^{2} = 8 \\ \\ d = 2, - 2$

A.P. – 3 , 5 , 7

OR

A.P. – 7 , 5 , 3