证明:x2+3/根号x2+1≥2根号2

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证明:x2+3/根号x2+1≥2根号2证明:x2+3/根号x2+1≥2根号2证明:x2+3/根号x2+1≥2根号2(x2+3/根号x2+1)^2-(2根号2)^2=(x^4-2x^2+1)/8(x^2

证明:x2+3/根号x2+1≥2根号2
证明:x2+3/根号x2+1≥2根号2

证明:x2+3/根号x2+1≥2根号2
(x2+3/根号x2+1)^2-(2根号2)^2
=(x^4-2x^2+1)/8(x^2+1)=(x^2-1)/8(x^2+1)>=0,
又因为不等式两边均为正,所以x2+3/根号x2+1≥2根号2