If x = 12−√3 find the value of x3 – 2x2 – 7x + 5

First, let's substitute the value of x into the equation.

x = 12 - √3

So, the equation x³ - 2x² - 7x + 5 becomes:

(12 - √3)³ - 2(12 - √3)² - 7(12 - √3) + 5

Now, let's simplify this step by step:

1. Calculate (12 - √3)³ = 1728 - 792√3 + 108 - 3 = 1833 - 792√3
2. Calculate 2(12 - √3)² = 2(144 - 24√3 + 3) = 294 - 48√3
3. Calculate 7(12 - √3) = 84 - 7√3

Substitute these values back into the equation:

1833 - 792√3 - 294 + 48√3 - 84 + 7√3 + 5 = 1460 - 737√3

So, the value of x³ - 2x² - 7x + 5 when x = 12 - √3 is 1460 - 737√3.