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?
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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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