The line x + y = 2 is tangent to the curve x^{2} = 3 - 2y at its point

x^{2 }= 3 – 2y

2x = 0 – 2 (dy / dx)

⇒ dy / dx = – x

The slope of the tangent of the curve is -x.

From the given information of the line,

the slope is -1. So, x = 1 and y = 1.

The required point is (1, 1)