Problems based on Numbers Test 1

Question : 3 of 40

Marks: +1, -0

The sum of the squares of three consecutive natural numbers is 2030, the second number is:

Solution:

Let three consecutive natural numbers be x, (x + 1) and (x + 2);
then,

x^2 + (x + 1)^2 + (x + 2)^2 = 2030

⇒ x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 2030

⇒3x^2 + 6x - 2025 = 0

⇒ x^2 + 2x - 675 = 0

⇒ (x + 27) (x - 25) = 0

Hence,

x = 25

∴ Second number = 25 + 1 = 26

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