Question

the product of two number is 12. the sum of both numbers is added to the square of both number is 32. find the number​

Answer 1

Let the numbers be X and Y.

Given X + Y = 3 -(a)

Given X^2 + Y^2 = 12 -(b)

Squaring (a) on both sides we get X^2 + Y^2 + 2XY = 9.

Putting (b) in this equation we get 2XY = -3 -(c)

Now consider (X-Y)^2 which is nothing but X^2 + Y^2 - 2XY, substituting (b) and (c) in this equation we get the value as 15.

(X-Y)^2 = 15 => (X - Y) = sqrt(15) -(d)

Now adding (a) and (d) we get 2*X = 3 + sqrt(15) => X = (3 + sqrt(15)) /2

Subtracting (a) and (d) we get 2*Y = 3 - sqrt(15) => Y = (3 - sqrt(15))/2

And there are your numbers!