Question

已知x=2m+n+2和x=m+2n時(shí)，多項(xiàng)式x²+4x+6的值相等，且m﹣n+2≠0，則當(dāng)x=3（m+n+1）時(shí)，多項(xiàng)式x²+4x+6的值等于　　．

Answer 1

3．

解析試題分析：先將x=2m+n+2和x=m+2n時(shí)，多項(xiàng)式x2+4x+6的值相等理解為x=2m+n+2和x=m+2n時(shí)，二次函數(shù)y=x²+4x+6的值相等，則可求拋物線的對(duì)稱軸為：；又二次函數(shù)y=x²+4x+6的對(duì)稱軸為直線x=-2，故可得出，化簡(jiǎn)得m+n=-2，所以當(dāng)x=3（m+n+1）=3×（-2+1）=-3時(shí)，x²+4x+6=3．
考點(diǎn)：二次函數(shù)的性質(zhì)．