Question

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

Answer 1

Let the nos be x and (x+2) becuz they are consecutive even nos .

so:(x+2)2 -x2 =36

  (x+2+x)(x+2-x)=36

  (2x+2)(2)=36

  2x+2=18

  2x=16

  x=8

Answer 2

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

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

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

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

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

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

$2x + 1 = 36$

$2x = 36 - 1 = 35$

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

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