Find the two points where the curve x^+xy+y^=7 crosses the x-axis, and show that the tangents to the curve at these points are parallel.

Please show me calulation

If you meant

x^2 + xy + y^2 = 7
then that is just an ellipse which has been rotated
The x-intercepts are at (-√7,0) and (√7,0)
To find the tangent slopes,
2x + y + xy' + 2yy' = 0
y' = -(2x+y)/(x+2y)
at the x-intercepts, the slopes are
-(-2√7)/-√7 = -2
-(2√7)/√7 = -2
so the lines are parallel