Given X=√5- 1, find the value of algebraic expression x 2+5x-6.

Scheme 1: Direct substitution calculation:

Original formula = (√ 5-1) 2+5 (√ 5-1)-6.

=6-2√5+5√5-5-6

=3√5-5。

Solution 2: (x+ 1) 2 = 5, x 2 =-2x+4, (reduction method)

Original formula =-2X+4+5X-6

=3X-2

=3(√5- 1)-2

=3√5-5。