Question

A number is devided in three parts which are in

a.p and the sum of there squares is 83 .find the smallest number

Answer 1

Dear friend,
Here's your answer...
Let the numbers be a-d , a, a+d.
As the sum of the numbers is 15.
So, a + d + a + a - d = 15
3a = 15
a = 5
As the sum of their squares is 83.
(a+d)² + a² + (a-d) ² = 83
a² + d² + 2ad + a² + a² + d² - 2ad = 83
3a² + 2d² = 83
3(5)² + 2d² = 83
75 + 2d² = 83
2d² = 83 - 75
2d² = 8
d² = 4
d = +_ 2
Therefore the numbers are: a-d = 5 - 2 = 3
a = 5 and a+d = 5 + 2 = 7.
Hence the smallest number is 3.
#Hope it helps you!!
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