If the roots of the equation `x^2+2c x+a b=0` are real unequal, prove that the equation `x^2-2(a+b)x+a^2+b^2+2c^2=0` has no real roots.

Explanation

To prove that the equation \( x^2 - 2(a+b)x + a^2 + b^2 + 2c^2 = 0 \) has no real roots given that the roots of the equation \( x^2 + 2cx + ab = 0 \) are real and unequal, we will follow these steps:

### Step 1: Determine the condition for real and unequal roots
For the quadratic equation \( x^2 + 2cx + ab = 0 \) to have real and unequal roots, the discriminant must be greater than zero. The discriminant \( D \) is given by:

\[ D = b^2 - 4ac \]
...