If point  P(x, y) is such that  y  =  x3 − 2x2 − 7x + 5&x  =  2 + √3 then point  P(x, y) is?

To find the coordinates of point P(x, y), we already have the x-coordinate given as x = 2 + √3.

We can find the y-coordinate by substitifying x = 2 + √3 into the equation y = x³ - 2x² - 7x + 5.

Step 1: Substitute x = 2 + √3 into the equation:

y = (2 + √3)³ - 2(2 + √3)² - 7(2 + √3) + 5

Step 2: Simplify the equation:

y = 8 + 12√3 + 9 - 8√3 - 2(4 + 4√3 + 3) - 14 - 7√3 + 5

Step 3: Continue to simplify:

y = 8 + 12√3 + 9 - 8√3 - 8 - 8√3 - 6 - 14 - 7√3 + 5

Step 4: Combine like terms:

y = 8 - 8 + 9 - 6 - 14 + 5 + 12√3 - 8√3 - 8√3 - 7√3

Step 5: Simplify further:

y = -6 + (-11√3)

So, the point P(x, y) is (2 + √3, -6 - 11√3).