Question

the square of the greater of the two consecutive even numbers exceeds the square of the smaller number by 36. find the number

Answer 1

two consecutive even numbers are 8 and 10

Answer 2

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$let \: no. \: be \: x \: and \: x + 1$

$there \: sq. \: are \: {x}^{2} \: and \: (x + 1 {)}^{2}$

$the \: diff. \: is \: 36$

$= > (x + 1 {)}^{2} - {x}^{2} = 36$

${x}^{2} + 2x + 1 - {x}^{2} = 36$

$\cancel{x}^{2} + 2x + 1 - \cancel {x}^{2} = 36$

$2x + 1 = 36$

$2x = 36 - 1 = 35$

$x = \cancel\frac{{35}}{2} = 17.5$

$so \: the \: no. \: are \: 17.5 \: and \: 18.5$