Question

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

Answer 1

SOLUTION :

Let the smaller number be x

The larger number be x + 2

The square of the greater number exceeds the square of the other by 36.

According to the problem,

(x + 2)² = x² + 36

x² + 2(x)(2) + 2² = x² + 36 [ (a + b)² = a² + 2ab + b² ]

x² + 4x + 4 = x² + 36

x² + 4x - x² = 36 - 4

4x = 32

x = 32/4

x = 8

Smaller Number = x = 8

Greater Number = x + 2 = 10

Therefore, the numbers are 10 and 8.

Answer 2

$\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \: the \: Question :}}}}\mid}$

$\: \: \: \:$

$\begin{gathered}:\implies\tt \Big( x + 2 \Big)^2 = 36 + x^2 \\\\\\:\implies\tt x^2 + 4 + 4x = 36 + x^2 \\\\\\:\implies\tt 4x + 4 = 36 \\\\\\:\implies\tt 4x = 36 - 4 \\\\\\:\implies\tt 4x = 32 \\\\\\:\implies\tt x = \dfrac{32}{4} \\\\\\:\implies\tt x = 8 \end{gathered}$

$\dag\:\underline{\textsf{Here we get value of x is \textbf{8}}}.†$

$\: \: \: \:$

$\begin{gathered}:\implies\tt \Big(x + 2 \Big) \\\\\\:\implies\tt 8 + 2 \\\\\\:\implies\huge\tt 10 \end{gathered}$

$\therefore\:\underline{\textsf{Required Numbers are \textbf{8 \& 10}}}.$