求函数y=x+1/2(x-1)^2(x>1)的最小值
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y=x+1/2(x-1)^2
= (2x+1/(x-1)^2)/2
= (2x-2+2+1/(x-1)^2)/2
= (x-1 + x-1 +1/(x-1)^2)/2 +1
≥3三次根号下(1) /2+1
=3/2+1
=5/2
= (2x+1/(x-1)^2)/2
= (2x-2+2+1/(x-1)^2)/2
= (x-1 + x-1 +1/(x-1)^2)/2 +1
≥3三次根号下(1) /2+1
=3/2+1
=5/2
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y=x+1/2(x-1)^2
=(x-1)+1/2(x-1)^2+1
=(x-1)/2+(x-1)/2+1/2(x-1)^2+1
≥3三次根号[(x-1)/2*(x-1)/2*1/2(x-1)^2]+1
=3/2+1
=5/2
=(x-1)+1/2(x-1)^2+1
=(x-1)/2+(x-1)/2+1/2(x-1)^2+1
≥3三次根号[(x-1)/2*(x-1)/2*1/2(x-1)^2]+1
=3/2+1
=5/2
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