分式的一些难题1、当a^2+b^2=3ab时,求[1+2b^2/(a^2-b^2)]*[1+2b/(a-b)]的值.2、当x^2-5x-2008=0时,求[(x-2)^3-(x-1)^2+1]/(x-2)的值.3、当ab=1,求1/(1+a^2)+1/(1+b^2)的值.(分式:“/”为除号,“^2”为平方,“^3”为立
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![分式的一些难题1、当a^2+b^2=3ab时,求[1+2b^2/(a^2-b^2)]*[1+2b/(a-b)]的值.2、当x^2-5x-2008=0时,求[(x-2)^3-(x-1)^2+1]/(x-2)的值.3、当ab=1,求1/(1+a^2)+1/(1+b^2)的值.(分式:“/”为除号,“^2”为平方,“^3”为立](/uploads/image/z/8626942-46-2.jpg?t=%E5%88%86%E5%BC%8F%E7%9A%84%E4%B8%80%E4%BA%9B%E9%9A%BE%E9%A2%981%E3%80%81%E5%BD%93a%5E2%2Bb%5E2%3D3ab%E6%97%B6%2C%E6%B1%82%5B1%2B2b%5E2%2F%28a%5E2-b%5E2%29%5D%2A%5B1%2B2b%2F%28a-b%29%5D%E7%9A%84%E5%80%BC.2%E3%80%81%E5%BD%93x%5E2-5x-2008%3D0%E6%97%B6%2C%E6%B1%82%5B%28x-2%29%5E3-%28x-1%29%5E2%2B1%5D%2F%28x-2%29%E7%9A%84%E5%80%BC.3%E3%80%81%E5%BD%93ab%3D1%2C%E6%B1%821%2F%281%2Ba%5E2%29%2B1%2F%281%2Bb%5E2%29%E7%9A%84%E5%80%BC.%EF%BC%88%E5%88%86%E5%BC%8F%EF%BC%9A%E2%80%9C%2F%E2%80%9D%E4%B8%BA%E9%99%A4%E5%8F%B7%EF%BC%8C%E2%80%9C%5E2%E2%80%9D%E4%B8%BA%E5%B9%B3%E6%96%B9%EF%BC%8C%E2%80%9C%5E3%E2%80%9D%E4%B8%BA%E7%AB%8B)
分式的一些难题1、当a^2+b^2=3ab时,求[1+2b^2/(a^2-b^2)]*[1+2b/(a-b)]的值.2、当x^2-5x-2008=0时,求[(x-2)^3-(x-1)^2+1]/(x-2)的值.3、当ab=1,求1/(1+a^2)+1/(1+b^2)的值.(分式:“/”为除号,“^2”为平方,“^3”为立
分式的一些难题
1、当a^2+b^2=3ab时,求[1+2b^2/(a^2-b^2)]*[1+2b/(a-b)]的值.
2、当x^2-5x-2008=0时,求[(x-2)^3-(x-1)^2+1]/(x-2)的值.
3、当ab=1,求1/(1+a^2)+1/(1+b^2)的值.
(分式:“/”为除号,“^2”为平方,“^3”为立方)分式的一些难题1、当a^2+b^2=3ab时,求[1+2b^2/(a^2-b^2)]*[1+2b/(a-b)]的值.2、当x^2-5x-2008=0时,求[(x-2)^3-(x-1)^2+1]/(x-2)的值.3、当ab=1,求1/(1+a^2)+1/(1+b^2)的值.(分式:“/”为除号,“^2”为平方,“^3”为立
1、
由a^2+b^2=3ab 得(a-b)^2=ab
原式={[a^2-b^2+2b^2]/(a+b)(a-b)}[(a-b+2b)/(a-b)]
={3ab/(a+b)(a-b)}[(a+b)/(a-b)]
=3ab/(a-b)^2
=3ab/ab
=3
2、
x^2-5x=2008
原式={(x-2+1)[x^2-4x+4-x+2+1]-(x-1)^2}/(x-2)
=(x-1)(x^2-4x+4-x+3-x+1)/(x-2)
=(x-1)(x^2-6x+8)/(x-2)
=(x-1)(x-2)(x-4)/(x-2)
=(x-1)(x-4)
=x^2-5x+4
=2008+4
=2012
3、
1/(1+a^2)+1/(1+b^2)
=ab/(ab+a^2)+ab/(ab+b^2)
=b/(a+b)+a/(a+b)
=(a+b)/(a+b)
=11 根据题意 a^2+b^2=3ab
可知 (a-b)^2=a^2+b^2-2ab=ab
原式=(a^2+b^2)/(a^2-b^2) +(a+b)/(a-b)
=(a^2+b^2)/(a-b)^2
=3ab/ab
=3
2
3 原式=(1+a^2+b^2+1)/(a^2b^2+a^2+b^2+1)
=(a^2+b^2+2)/(a^2+b^2+2)
=1