Question

A number 15 is divided into 3 parts which are in A.P. and sum of their squares is 83. The smallest part is
a) 5
b) 3
c) 6
d) 2
e) Option 5

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Answer 1

Answer:-

Let the numbers be a - d , a , a + d.

Given:

Sum of the numbers = 15

→ a - d + a + a + d = 15

→ 3a = 15

→ a = 15/3

→ a = 5

And,

Sum of their squares = 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 = 8/2

→ d² = 4

→ d = ± 2.

If d = + 2 ;

→ a - d = 5 - 2 = 3

→ a = 5

→ a + d = 5 + 2 = 7.

If d = - 2 ;

→ a - d = 5 -( - 2) = 7

→ a = 5

→ a + d = 5 + ( - 2) = 3.

Hence, the smallest number/Part is 3(b).

Answer 2

your answer is = OPTION b (3)

hope it helps

bye....