Horns Of A Number

Let the two number be a , b . According to the question, $a + b = 10$ and $ab=40$ .

We can this assume a quadratic equation whose roots are a and b . Using Vieta's formula, The quadratic formed will be ,

$x^2 - (sum of roots ) x + (product of roots ) = 0$

$x^2 - 10x + 40 =0$

a and b are the roots of the equation and thus it must satisfy the equations , Hence we get ,

$b^2 -10b + 40 = 0$

$b^2 = 10b -40$

Now we need to find the value of ,

$K(let) = 10a + b^2 = 10a + 10b - 40$

So , $K = 10(a + b) - 40 = 100 - 40 = 60$

$\boxed{K = 60 }$