[1+12/(3x+y)]√x=2,[1-12/(3x+y)]√y=6解方程组

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[1+12/(3x+y)]√x=2,[1-12/(3x+y)]√y=6解方程组[1+12/(3x+y)]√x=2,[1-12/(3x+y)]√y=6解方程组[1+12/(3x+y)]√x=2,[1-1

[1+12/(3x+y)]√x=2,[1-12/(3x+y)]√y=6解方程组
[1+12/(3x+y)]√x=2,[1-12/(3x+y)]√y=6
解方程组

[1+12/(3x+y)]√x=2,[1-12/(3x+y)]√y=6解方程组
[1+12/(3x+y)]√x=2, 1+12/（3x+y)=2/√x,①
[1-12/(3x+y)]√y=6,1-12/(3x+y)=6/√y.②
(①+②)/2,得1=1/√x+3/√y,
(√x-1)/√x=3/√y,
∴√y=3√x/(√x-1),③
(①-②)/2,得12/(3x+y)=1/√x-3/√y=(2-√x)/√x,
∴3x+y=12√x/(2-√x),④
把③代入④,3x+[3√x/(√x-1)]^2=12√x/(2-√x),
设u=√x>0,上式变为3u^2+[3u/(u-1)]^2=12u/(2-u),
两边都乘以(2-u)(u-1)^2/(3u),得u(2-u)(u-1)^2+3u(2-u)=4(u-1)^2,
整理得u^4-4u^3+12u^2-16u+4=0,
解得u1≈1.68125,u2≈0.31875(舍),或u^2-2u+7.464102≈0（无实根),
代入③,√y=7.403669,
∴x≈2.82660,y≈54.8143.

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