Question

The square of the greater of two consecutive even numbers exceeds the square of the smaller by 36. Find the numbers.

Answer 1

Let the two numbers be 2x and (2x+2)

Squares=4x² and (2x+2)²

As per question, (2x+2)²-4x²=36

4x²+8x+4-4x²=36

8x+4=36

8x=32

x=4

∴The two numbers are 8 and 10.

Answer 2

$\huge {\boxed {\fcolorbox{pink}{red} {\purple{ur\:answer}}}}$

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

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

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

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

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

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

$2x + 1 = 36$

$2x = 36 - 1 = 35$

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

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