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  4. The sum of two numbers is 17 and the sum of their squares is 157 . Find the number.

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Q. The sum of two numbers is 17 and the sum of their squares is 157 . Find the number.

Quadratic Equations

Solution:

Let the numbers be $x$ and $(17-x)$
According to the given information,
$x^2+(17-x)^2 =157$
$x^2+289+x^2-34 x =157 $
$2 x^2-34 x+132 =0 $
$x^2-17 x+66 =0$
$x^2-11 x-6 x+66 =0 $
$x(x-11)-6(x-11) =0 $
$(x-11)(x-6) =0 $
$x =11,6$