Question

The sum of three numbers in A.P. is 42. If the sum of their squares is 596
what is the largest of the three numbers?​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer :-

Let us assume that, the three numbers in AP are (a - d) , a , (a + d) .

so,

→ (a - d) + a + (a + d) = 42

→ 3a = 42

→ a = 14 .

then,

→ (14 - d)² + 14² + (14 + d)² = 596

→ 196 + d² - 28d + 196 + 196 + d² + 28d = 596

→ 2d² = 596 - 588

→ 2d² = 8

→ d² = 4

→ d = ±2 .

when d = 2 ,

• Largest number = 14 + 2 = 16 .

when d = (-2) ,

• Largest number = 14 - 2 = 12 .
• second number = 10
• third number = 8
• sum ≠ 42

therefore, largest number is 16.

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