设实数xy满足4x²-5xy+4y²=5,令S=x²+y²,则1/smax+1/smin=快啊sos

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设实数xy满足4x²-5xy+4y²=5,令S=x²+y²,则1/smax+1/smin=快啊sos

设实数xy满足4x²-5xy+4y²=5,令S=x²+y²,则1/smax+1/smin=快啊sos
设实数xy满足4x²-5xy+4y²=5,令S=x²+y²,则1/smax+1/smin=
快啊sos

设实数xy满足4x²-5xy+4y²=5,令S=x²+y²,则1/smax+1/smin=快啊sos
x=√s cosB y=√s sinB
4x^2-5xy+4y^2=5
4(√s cosB)^2-5√s cosB*√s sinB+4(√s sinB)^2=5
4s (cosB)^2-5s sinBcosB+4s (sinB)^2=5
4s-5s/2 sin2B=5
s=5/(4-5/2 sin2B)∈[10/13,10/3]
1/smax+1/smin=3/10+13/10=8/5