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`(3+2x)/(2+3x) = 12/13 - 5/(13x) (x \ne (-2)/3; x \ne 0)`
`-> (3+2x)/(2+3x) = (12x)/(13x) - 5/(13x)`
`->(3+2x)/(2+3x) = (12x - 5)/(13x)`
`-> (2 +3x) (12x - 5) = (3+2x).13x`
`-> 24x - 10 + 36x^2 - 15x = 39x + 26x^2`
`-> 36x^2 + 9x - 10 - 26x^2 - 39x=0`
`-> 10x^2 - 30x - 10=0`
`-> 10 (x^2 - 3x - 1)=0`
`->x^2 -3x-1=0`
`->x^2 - 2 . x . 3/2 + (3/2)^2 -13/4=0`
`-> (x-3/2)^2 = 13/4`
TH1 :
`(x-3/2)^2=(\sqrt{13/4})^2`
`-> x-3/2=\sqrt{13/4}`
`->x=(3+\sqrt{13})/2` (tm)
TH2 :
`(x-3/2)^2=(-\sqrt{13/4})^2`
`->x-3/2=-\sqrt{13/4}`
`->x=(3-\sqrt{13})/2` (tm)
Vậy `x=(3+\sqrt{13})/2` hoặc `x=(3-\sqrt{13})/2`
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Ta chứng minh :
`(a+b)^2 = a^2 +2ab + b^2`
Vế trái :
`=a^2 + ab+ab+b^2`
`=(a^2+ab)+(ab+b^2)`
`=a(a+b)+b(a+b)`
`=(a+b)(a+b)`
`=(a+b)^2` (Đpcm)
