Toán Lớp 8: Chứng minh với x $\neq$ ±1 thì:
(x^2 + x + 1 + 2/{x-1})(x^2-x+1-2/{x+1})=(x^2+x+1)(x^2-x+1)
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Toán Lớp 8: Chứng minh với x $\neq$ ±1 thì:
(x^2 + x + 1 + 2/{x-1})(x^2-x+1-2/{x+1})=(x^2+x+1)(x^2-x+1)
Comments ( 1 )
Ta có:
VT=(x^2+x+1+2/(x-1))(x^2-x+1-2/(x+1))
VT=(((x^2+x+1)(x-1))/(x-1)+2/(x-1))(((x^2-x+1)(x+1))/(x+1)-2/(x+1))
VT=((x^3-1)/(x-1)+2/(x-1))((x^3+1)/(x+1)-2/(x+1))
VT=((x^3-1+2)/(x-1))((x^3+1-2)/(x+1))
VT=(x^3+1)/(x-1) . (x^3-1)/(x+1)
VT=((x+1)(x^2-x+1))/(x-1) . ((x-1)(x^2+x+1))/(x+1)
VT=(x^2-x+1)(x^2+x+1)=VP(text{ĐPCM})
Vậy (x^2+x+1+2/(x-1))(x^2-x+1-2/(x+1))=(x^2+x+1)(x^2-x+1)(x\ne+-1)