已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 11:31:01

已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=
已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=

已知实数a,b满足(a+b)^2=2b^2+ab且a,b同号,则a+b/a-b=
(a+b)^2=2b^2+ab
所以a^2+2ab+b^2=2b^2+ab
a^2-ab=b^2
a(a-b)=b^2
b/(a-b)=a/b
又a^2-ab=b^2
所以a^2-ab-b^2=0
把a看作未知数
a=(b±√5b^2)/2=b(1±√5)/2
a/b=(1±√5)/2
ab同号,所以a/b>0
a/b=(1+√5)/2
(a+b)/(a-b)=(a-b+2b)/(a-b)
=(a-b)/(a-b)+2b/(a-b)
=1+2b/(a-b)
=1+2a/b
=1+1+√5
=2+√5

(a+b)^2=2b^2+ab
所以a^2+2ab+b^2=2b^2+ab
a^2-ab=b^2
所以a(a-b)=b^2
a^2=b(a+b)
a+b/a-b=a^3/b^3

(a+b)/(a-b)=(a-b+2b)/(a-b)
=(a-b)/(a-b)+2b/(a-b)
=1+2b/(a-b)
=1+2a/b
=1+1+√5
=2+√5

已知实数a、b满足实数(a+b)^2+a+b-2=0,求a+b的值已知实数a,b满足a>b,求证：-a^2-a＜-b^3-b 已知实数a,b满足|a|=b,|ab|+ab=0,化简|a|+|-2b|-|3b-2a| 已知实数a,b 满足|a|=b ,|ab|+ab=0 化简：|a|+|-2b|-|3b-2a| 已知实数a,b满足：a+b=1,ab=-2,求b/a+a/b的值. 已知实数a,b满足(a+b)的平方+a+b-2=0,求a+b的值已知实数a b.满足(a+b)平方+a+b-2=0求a+b的值已知实数a、b满足(a+b)方+a+b-2=0,求a+b的值已知实数a b 满足a+b+10=6 √a + 2 √b,求a,b的值已知实数a,b满足a'2+2a=2,b'2=2b=2,且a≠b,求b/a+a/b=？已知实数a,b满足a^2=2-2a,b^2=2-2b,且a不等于b,求b/a+a/b的值已知实数a,b满足a²+2a=2,b²+2b=2,且a≠b,求b/a+a/b的值已知：实数a、b（a≠b)满足a^2-7a+5=0,b^2-7b+5=0,则b/a+a/b=? 已知实数a.b满足a*a-3a=1,b*b-3b=1,求2b/a+2a/b的值已知实数A,B满足A+B=2;AB=1,求代数式的值已知实数a,b,满足a2+b2=2,则a,b最大值为已知实数a,b满足（a-2）+√b-2a=0,求b-a的平方根已知实数a,b满足a平方-2a+6b=5,则a+3b的最大值是多少