1.
若\( \displaystyle x=\sqrt{x-\frac{1}{x}}+\sqrt{1-\frac{1}{x}} \)，求\( x= \)？
https://math.pro/db/viewthread.php?tid=1492&page=2#pid7156
5.
設x,y為複數，且滿足聯立方程組\( \Bigg\{\; \matrix{x+y=5 \cr x^4+y^4=97} \)，試求數對\( (x,y)= \)？
連結有算式
(95中壢高中，h ttp://forum.nta.org.tw/examservice/showthread.php?t=555連結已失效)
[解答]
\( x^2+2xy+y^2=25 \)
\( (x^2+y^2)^2=(25-2xy)^2 \)
\( x^4+2x^2y^2+y^4=625-100xy+4x^2y^2 \)
\( 97+2x^2y^2=625-100xy+4x^2y^2 \)
\( x^2y^2-50xy+264=0 \)
\( xy=6 or 44 \)
(1)
\( \displaystyle \Bigg\{\; \matrix{x+y=5 \cr xy=6} \)
\( \displaystyle \Bigg\{\; \matrix{x=2 \cr y=3} \)or\( \displaystyle \Bigg\{\; \matrix{x=3 \cr y=2} \)
(2)
\( \displaystyle \Bigg\{\; \matrix{x+y=5 \cr xy=44} \)
\( \displaystyle \Bigg\{\; \matrix{x=\frac{5+\sqrt{151}i}{2} \cr y=\frac{5-\sqrt{151}i}{2}} \)or\( \displaystyle \Bigg\{\; \matrix{x=\frac{5-\sqrt{151}i}{2} \cr y=\frac{5+\sqrt{151}i}{2}} \)
共四組解
