Cho (a^2 - bc )( b - abc ) = ( b^2 - ac )( a - abc ) ; abc khác 0 ; a khác b
CMR : [tex]\frac{1}{a}[/tex] + [tex]\frac{1}{b}[/tex] + [tex]\frac{1}{c}[/tex] = a + b + c
Có
(a^2-bc)(b-abc)=(b^2-ac)(a-abc)
-> a^2b-b^2c-a^3bc+ab^2c^2=ab^2-a^2c-ab^3c+a^2bc^2
-> a^2b-b^2c-b^2a+a^2c=a^3bc-ab^2c^2-ab^3c+a^2bc^2
-> ab(a-b)+c(a^2-b^2)=abc(a^2-b^2)+abc^2(a-b)
-> (a-b)(ab+ac+bc)=abc(a-b)(a+b+c)
-> (a-b)(ab+ac+bc) / abc(a-b)=abc(a-b)(a+b+c) / abc(a-b) ( chia cả 2 vê cho abc(a-b))
-> (ab+ac+bc)/abc=a+b+c
-> ab/abc+bc/abc+ca/abc=a+b+c
-> 1/a+1/b+1/c=a+b+c(dcpcm)
![Big Grin :D :D](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)