Question

The average of the squares of two consecutive positive even numbers is 626. Find the numbers.​

Answer 1

$let \: one \: no. \: be \: x \\ other \: no. = x + 2$

ATQ,

$\frac{ {x}^{2} + {(x + 2)}^{2} }{2} = 626 \\ {x}^{2} + {x}^{2} + 4x + 4 = 626 \times 2 \\ 2 {x}^{2} + 4x + 4 = 1252 \\ 2 {x}^{2} + 4x + 4 - 1252 = 0 \\ 2 {x}^{2} + 4x - 1248 = 0 \\ {x}^{2} + 2x - 624 = 0 \\ {x}^{2} + 26x - 24x - 624 = 0 \\ x(x + 26) - 24(x + 26) = 0 \\ (x - 24)(x + 26) = 0 \\ x = 24 \: or \: - 26$

Since x is a positive even integer,

first no. = x = 24

second no. = x + 2 = 24 + 2 = 26

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