设A=1+2x*x*x*x,b=2x*x*x+x*x,x为实数不等于1,比较A,B大小要求有具体过程
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![设A=1+2x*x*x*x,b=2x*x*x+x*x,x为实数不等于1,比较A,B大小要求有具体过程](/uploads/image/z/5195673-9-3.jpg?t=%E8%AE%BEA%3D1%2B2x%2Ax%2Ax%2Ax%2Cb%3D2x%2Ax%2Ax%2Bx%2Ax%2Cx%E4%B8%BA%E5%AE%9E%E6%95%B0%E4%B8%8D%E7%AD%89%E4%BA%8E1%2C%E6%AF%94%E8%BE%83A%2CB%E5%A4%A7%E5%B0%8F%E8%A6%81%E6%B1%82%E6%9C%89%E5%85%B7%E4%BD%93%E8%BF%87%E7%A8%8B)
设A=1+2x*x*x*x,b=2x*x*x+x*x,x为实数不等于1,比较A,B大小要求有具体过程
设A=1+2x*x*x*x,b=2x*x*x+x*x,x为实数不等于1,比较A,B大小
要求有具体过程
设A=1+2x*x*x*x,b=2x*x*x+x*x,x为实数不等于1,比较A,B大小要求有具体过程
A=1+2x×x×x×x=2X^4+1
B=2x×x×x+x×x=2X^3+X^2
A-B=2X^4+1-(2X^3+X^2)
=2X^4-2X^3-X^2+1
=2X^3(X-1)-(X-1)(X+1)
=(X-1)(2X^3-X-1)
=(X-1)(X-1)(2X^2+2X+1)
=(X-1)^2×[X^2+(X+1)^2]
而x为实数不等于1,所以(X-1)^2>0,X^2+(X+1)^2>0
即A-B>0
故A>B
A=1+2x*x*x*x=2X^4+1
B=2x*x*x+x*x=2X^3+X^2
A-B=2X^4+1-(2X^3+X^2)
=2X^4-2X^3-X^2+1
=2X^3(X-1)-(X-1)(X+1)
=(X-1)(2X^3-X-1)
=(X-1)(X-1)(2X^2+2X+1)
=(X-1)^2*[X^2+(X+1)^2]
因为x为实数不等于1,所以A-B>0
A>B