Alg3.2.13

The sum of the squares of two positive integers is 208.If the square of the larger number is 18 times the smaller number,find the numbers.

Let $x\,$ be the smaller number

The square of the larger number is $18x\,$

Therefore, $x^2+18x=208\,$

$x^2+18x-208=0\,$

$x^2+26x-8x-208=0,x(x+26)-8(x+26)=0,(x+26)(x-8)=0\,$

$x=-26,8\,$ given is the positive integers,hence the value of x is 8.

The shorter number is 8.

The larger number is $\sqrt{18\cdot 8}=\sqrt{144}=12\,$