⑴等腰直角三角形的面积:1/2*X*1/2X=1/4X^2,
XY+1/4X^2=8
Y=(8-1/4X^2)/X=8/X-X/4,
(0
=(√2+2)X+16/X-1/2X
=(√2+3/2)X+16/X
≥2√[(√2+3/2)X*16/X]
=2√[8(2√2+3)]
=2√8*√(1+√2)^2
=4(2+√2)。
当且仅当(√2+3/2)X=16/X时,取等号,
X^2=32/(2√2+3)
X=4√2/(√2+1)=4√2(√2-1)=8-4√2,
Y=8/X-X/4
=2+√2-(2-4√2)
=5√2。
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