Trignometry - 8

Geometry Level 4

If \( 0 \leq p \leq 3 , 0 \leq q \leq 3\) and the equation \[ x^2 + 4 + 3 \cos(px+q) = 2x \] has atleast one solution and the value of \( p+q = \dfrac{k\pi}{4} \), then what is the minimum positive value of k?

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