If show that the value of x³ - 2x² - 7x + 5 is 3.

Or

Simplify:

Now, x² = (2 + √3)² = 4 + 3 + 4√3 = 7 + 4√3

Also, x³ = x × x² = (2 + √3)(7 + 4√3)

= 2(7) + 7(√3) + 2(4√3) + (√3)(4√3)

= 14 + 15√3 + 12

= 26 + 15√3

Put all the values in the expression: x³ - 2x² - 7x + 5

= (26 + 15√3)-2(7 + 4√3)-7(2 + √3) + 5

= 3

rationalize-

= √2-1 + √3-√2 + …√8-√7 + √9-√8

= √9-1

= 3-1

= 2