已知(3x+5)/(x^2-4)=a/(x-2)+b/(x+2) ,那么 a^2+b^2=

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已知(3x+5)/(x^2-4)=a/(x-2)+b/(x+2) ,那么 a^2+b^2=
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已知(3x+5)/(x^2-4)=a/(x-2)+b/(x+2) ,那么 a^2+b^2=
已知(3x+5)/(x^2-4)=a/(x-2)+b/(x+2) ,那么 a^2+b^2=

已知(3x+5)/(x^2-4)=a/(x-2)+b/(x+2) ,那么 a^2+b^2=
(3x+5)/(x^2-4)=a/(x-2)+b/(x+2)
(3x+5)/(x^2-4)=[a(x+2)+b(x-2)]/(x²-4)
(3x+5)/(x^2-4)=【(a+b)x+(2a-2b)】/(x²-4)
所以:a+b=3
2a-2b=5
解得:a=11/4 ,b=1/4
a²+b²=122/16=61/8

(3x+5)/(x^2-4)=a/(x-2)+b/(x+2)
(3x+5)=(a+b)x+2(a-b)
a+b=3
a-b=5/2
a^2+b^2=61/8

a=1/4,b=11/4,a^2+b^2=7.625

(3x+5)/(x^2-4)=a/(x-2)+b/(x+2)
(3x+5)/(x^2-4)={a(x+2)+b(x-2)}/(x^2-4)
(3x+5)/(x^2-4)={(a+b)+2(a-b)}/(x^2-4)
a+b=3,a-b=5/2
(a+b)^2+(a-b)^2=3^2+(5/2)^2
2(a^2+b^2)= 61/4
a^2+b^2= 61/8

3x+5=a(x+2)+b(x-2)
3x+5=(a+b)x+(2a-2b)
a+b=3 2a-2b=5
a=2.75 b=0.25
a^2+b^2=7.625