X(√y)+ (√x)y-(√2003x)-(√2003y)+(√2003xy)=2003求正整数xy的值如题上题不用了帮我解这题已知√(7x^2+9x+13)+√(7x^2-5x+13)=7x
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![X(√y)+ (√x)y-(√2003x)-(√2003y)+(√2003xy)=2003求正整数xy的值如题上题不用了帮我解这题已知√(7x^2+9x+13)+√(7x^2-5x+13)=7x](/uploads/image/z/13898809-1-9.jpg?t=X%28%E2%88%9Ay%29%2B+%28%E2%88%9Ax%29y-%28%E2%88%9A2003x%EF%BC%89-%28%E2%88%9A2003y%EF%BC%89%2B%28%E2%88%9A2003xy%EF%BC%89%3D2003%E6%B1%82%E6%AD%A3%E6%95%B4%E6%95%B0xy%E7%9A%84%E5%80%BC%E5%A6%82%E9%A2%98%E4%B8%8A%E9%A2%98%E4%B8%8D%E7%94%A8%E4%BA%86%E5%B8%AE%E6%88%91%E8%A7%A3%E8%BF%99%E9%A2%98%E5%B7%B2%E7%9F%A5%E2%88%9A%EF%BC%887x%5E2%2B9x%2B13%EF%BC%89%2B%E2%88%9A%EF%BC%887x%5E2-5x%2B13%EF%BC%89%3D7x)
X(√y)+ (√x)y-(√2003x)-(√2003y)+(√2003xy)=2003求正整数xy的值如题上题不用了帮我解这题已知√(7x^2+9x+13)+√(7x^2-5x+13)=7x
X(√y)+ (√x)y-(√2003x)-(√2003y)+(√2003xy)=2003求正整数xy的值
如题
上题不用了
帮我解这题
已知√(7x^2+9x+13)+√(7x^2-5x+13)=7x
X(√y)+ (√x)y-(√2003x)-(√2003y)+(√2003xy)=2003求正整数xy的值如题上题不用了帮我解这题已知√(7x^2+9x+13)+√(7x^2-5x+13)=7x
(√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