M属于[-1,+1],X属于[-根2/2,根2/2],求证|2X^2+mX-1|<=9/8.(

f(x)=2x^2+mx-1=2(x+m/4)^2-1-m^2/8
f(x)的对称轴-m/4∈[-1/4,1/4]
在x∈[-(√2)/2,(√2)/2]上
最大值f(√2/2)或f(-√2/2)
最小值f(-m/4)
f(-m/4)≤f(x)≤max{f(√2/2),f(-√2/2)}
|f(x)|≤max{|f(-m/4)|,|f(√2/2)|,|f(-√2/2)|}
=max{|-1-m^2/8|,|√2/2m|}
≤max{|-1-1^2/8|,|√2/2|}
=9/8
当m=1 or -1时|f(-m/4)|=9/8