Author Archives: kevin

Find all real solutions of the following equations: $$a+b=c^2$$ $$b+c=d^2$$ $$c+d=e^2$$ $$d+e=a^2$$ $$e+a=b^2$$ Solution: If $a=b=c=d=e$, then we have two real solutions as $$a=b=c=d=e=0$$ and $$a=b=c=d=e=2$$ Without loss of generality, assume $a\le b \le c \le d \le e$ and … Continue reading →

Find real solutions for the following equations: $$a+bcd = 2$$ $$b+cda=2$$ $$c+dab=2$$ $$d + abc=2$$ Solution: Because $a+bcd=2$, $b+cda=2$, we have $a+bcd=b+cda$. Factorizing it, we have $$(a-b)(cd-1)=0$$ Therefore either $a=b$ or $cd=1$. Case 1: If $a=b$, we have $$a+ac^2=2$$ $$c+da^2=2$$ … Continue reading →