Question

已知X=√2-1化简(3+2√2)X²-(√2+1)X+4？

Answer 1

因为x=√2-1，这样就有x²=(√2-1)²=3-2√2，(√2+1)x=(√2+1)*(√2-1)=1，由此可知，(3+2√2)x²-(√2+1)x+4就等于(3+2√2)*(3-2√2)-1+4=3²-(2√2)²-1+4=9-8-1+4=4。

Answer 2

解：当X=√2-1时，
(3+2√2)X²-(√2+1)X+4
=(√2+1)²X²-(√2+1)X+4
=[(√2+1)X-1/2]²+15/4
=[(√2+1)(√2-1)-1/2]²+15/4
=1/4+15/4
=4