If `xa n dy` are positive acute angles such that `(x+y)` and `(x-y)` satisfy the equation `tan^2theta-4tantheta+1=0,` then `x=pi/6` (b) `y=pi/4` (c) `y=pi/6` (d) `y=pi/4`

Explanation

To solve the problem, we need to find the values of the angles \( x \) and \( y \) given that \( x + y \) and \( x - y \) satisfy the equation:

\[ \tan^2 \theta - 4 \tan \theta + 1 = 0 \]

### Step 1: Identify the roots of the quadratic equation
The given equation is a quadratic in terms of \( \tan \theta \). We can use the quadratic formula to find the roots:
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