①若ab=1则(1/1+a²)+(1/1+b²)的值为?②若x+(1/x)=5则x²+x+(1/x²)+1/x的值为?
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![①若ab=1则(1/1+a²)+(1/1+b²)的值为?②若x+(1/x)=5则x²+x+(1/x²)+1/x的值为?](/uploads/image/z/3936565-37-5.jpg?t=%E2%91%A0%E8%8B%A5ab%3D1%E5%88%99%281%2F1%2Ba%26%23178%3B%29%2B%281%2F1%2Bb%26%23178%3B%29%E7%9A%84%E5%80%BC%E4%B8%BA%3F%E2%91%A1%E8%8B%A5x%2B%281%2Fx%29%3D5%E5%88%99x%26%23178%3B%2Bx%2B%281%2Fx%26%23178%3B%29%2B1%2Fx%E7%9A%84%E5%80%BC%E4%B8%BA%3F)
①若ab=1则(1/1+a²)+(1/1+b²)的值为?②若x+(1/x)=5则x²+x+(1/x²)+1/x的值为?
①若ab=1则(1/1+a²)+(1/1+b²)的值为?
②若x+(1/x)=5则x²+x+(1/x²)+1/x的值为?
①若ab=1则(1/1+a²)+(1/1+b²)的值为?②若x+(1/x)=5则x²+x+(1/x²)+1/x的值为?
(1/1+a²)+(1/1+b²)=(ab/ab+a²)+(ab/ab+b²)
=b/a+b+(a/a+b)
=a+b/a+b=1
x²+x+(1/x²)+1/x=x²+1/x²+x+1/x
=(x+1/x)²-2+5
=28
1) 因为ab=1 所以b=1/a
1/(1+a^2)+1/(1+b^2)
=1/(1+a^2)+1/(1+1/a^2)
=1/(1+a^2)+(a^2)/(1+a^2)
=1
2) x^2+x+1/x^2+1/x
=(x+1/x)^2+ (x+1/x)-2
=5^2+5-2
=28
(1/1+a²)+(1/1+b²)
通分=(1+b²+1+a²)/(1+a²)(1+b²)
=(2+a²+b²)/(1+a²+b²+a²b²)
=(2+a²+b²)/(2+a²+b²)
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(1/1+a²)+(1/1+b²)
通分=(1+b²+1+a²)/(1+a²)(1+b²)
=(2+a²+b²)/(1+a²+b²+a²b²)
=(2+a²+b²)/(2+a²+b²)
=1
② x+(1/x)=5 两边平方得:x²+2+(1/x²)=25
x²+1/x²=25-2=23
x²+x+(1/x²)+1/x=x²+1/x²+x+(1/x)=23+5=28
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