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If the square of sum of three positive consecutive natural numbers exceeds the sum of their corresponding squares by 484 then what is the largest of the three numbers? 
  • a)
  • b)
  • c)
  • d)
    10 
Correct answer is option 'D'. Can you explain this answer?
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Given Information:
- Let the three consecutive natural numbers be x, x+1, and x+2.

Given Condition:
- The square of the sum of the three numbers exceeds the sum of their squares by 484.

Formulas:
- Sum of the three numbers: x + x+1 + x+2 = 3x + 3
- Square of the sum of the three numbers: (3x + 3)^2
- Sum of their squares: x^2 + (x+1)^2 + (x+2)^2

Equation:
- (3x + 3)^2 = x^2 + (x+1)^2 + (x+2)^2 + 484

Solve the Equation:
- Expand the left side: 9x^2 + 18x + 9 = x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 + 484
- Simplify: 9x^2 + 18x + 9 = 3x^2 + 6x + 489
- Rearrange: 6x^2 + 12x - 480 = 0
- Divide by 6: x^2 + 2x - 80 = 0
- Factorize: (x + 10)(x - 8) = 0
- The possible values for x are -10 and 8. Since the numbers are positive, x = 8.

Calculate the Largest Number:
- Largest number = x + 2 = 8 + 2 = 10
Therefore, the largest of the three numbers is 10. Hence, the correct answer is option 'D'.
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If the square of sum of three positive consecutive natural numbers exceeds the sum of their corresponding squares by 484 then what is the largest of the three numbers?a)7b)8c)9d)10Correct answer is option 'D'. Can you explain this answer?
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