Show that the equation `2(a^2+b^2)x^2+2(a+b)x+1=0` has no real roots, when `a!=bdot`

Explanation

To show that the equation \( 2(a^2 + b^2)x^2 + 2(a + b)x + 1 = 0 \) has no real roots when \( a \neq b \), we will analyze the discriminant of the quadratic equation.

### Step 1: Identify the coefficients
The given quadratic equation can be written in the standard form \( ax^2 + bx + c = 0 \).
Here, we identify:
- \( a = 2(a^2 + b^2) \)
- \( b = 2(a + b) \)
- \( c = 1 \)
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