Question

不等式解答题 p=1+2(x²）²; Q=2x³;+x²; 比较p Q大小 ..

Answer 1

设 P-Q=1+2*x^4-2*x^3-x^2=(2*x^2+a*x+1)*(x^2+b*x+1)

右边展开= 2*x^4 + (a + 2*b)*x^3 + (a*b + 3)*x^2 + (a + b)*x + 1

与左边比较可得：

a+2b=-2

a+b=0

解得 a=2,b=-2

所以

P-Q=1+2*x^4-2*x^3-x^2

=(2*x^2+2*x+1)*(x^2-2*x+1)

=(2*x^2+2*x+1)*(x-1)^2

=[2(x+1/2)^2+1/2]*(x-1)^2 恒大于>0

所以 P>Q