(√xy)(√x+√y)-(√2003)(√x+√y)+(√2003)(√xy)-(√2003)^2=0
(√x+√y)(√xy-√2003)+(√2003)(√xy-√2003)=0
(√x+√y+√2003)(√xy-√2003)=0
xy=2003
x,y是2003的约数.
x=1,y=2003
√(7x^2+9x+13)+√(7x^2-5x+13)=7x (1)
=[7x^2+9x+13)-(7x^2-5x+13)]/2
=[√(7x^2+9x+13)+√(7x^2-5x+13)][√(7x^2+9x+13)-√(7x^2-5x+13)]/2
√(7x^2+9x+13)-√(7x^2-5x+13)=2
与(1)相加
2√(7x^2+9x+13)=7x+2
其中,要不等式有意义,x>-2/7
4(7x^2+9x+13)=(7x+2)^2
整理,得:
21x^2-8x-48=0
(3x+4)(7x-12)=0
x=-4/3(舍去)或x=12/7
x=12/7