# The sum of the squares of two positive numbers is 53 and the difference of the squares of the numbers is 45. How do you find the number?

Nov 26, 2016

$7 , 2$

#### Explanation:

Let the two numbers be $a \mathmr{and} b$, repectively.

$\implies {a}^{2} + {b}^{2} = 53 - - - - \left(1\right)$
$\implies {a}^{2} - {b}^{2} = 45 - - - - \left(2\right)$

$\left(1\right) + \left(2\right) \implies 2 {a}^{2} = 98$
$\implies {a}^{2} = 49$
$\implies a = \pm 7$
$\implies b = \pm 2$

Given that $a$ and $b$ are both positive,
hence, $a = 7 , b = 2$

Check :

${7}^{2} + {2}^{2} = 49 + 4 = 53$
${7}^{2} - {2}^{2} = 49 - 4 = 45$