My problems from Magazine
Solve:a.$x^{3}+ x+ 6= 2 ( x+ 1 )\sqrt{3+ 2x- x^{2}}$
b.
$\frac{1}{\sqrt{x}}+ \frac{1}{\sqrt{y}}+ \frac{1}{\sqrt{z}} = 3$
$\frac{x^{2}}{y}+ \frac{y^{2}}{z}+ \frac{z^{2}}{x} = \root{4}{\frac{x^{4}+ y^{4}}{2}} + \root{4}{\frac{y^{4}+ z^{4}}{2}}+\root{4}{\frac{z^{4}+ x^{4}}{2}}$
第一题可以变量替换$x=1+2\sin(t), -\pi/2<=t<=\pi/2$
于是变成$12\sin^2(t)(2/3sin(t)+ 1) + 8(1-\cos(t))(\sin(t)+1)=0$
显然只能有唯一解$\sin(t)=0$即$x=1$
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