(x+y)(x-y)-9y^2=(x-2y)(x+5y)-3xy chung minh dang thuc 28/07/2021 Bởi Remi (x+y)(x-y)-9y^2=(x-2y)(x+5y)-3xy chung minh dang thuc
Xét $VT$: $(x+y)(x-y)-9y^2$ $=x^2-y^2-9y^2$ $=x^2-10y^2$ (1) Xét $VP$: $(x-2y)(x+5y)-3xy$ $=x(x+5y)-2y(x+5y)-3xy$ $=x^2+5xy-2xy-10y^2-3xy$ $=x^2+(5xy-2xy-3xy)-10y^2$ $=x^2-10y^2$ (2) Từ (1), (2) $→VT=VP$ (ĐPCM) Bình luận
`(x+y)(x-y)-9y²=(x-2y)(x+5y)-3xy` `⇒ x²-y²-9y²=x²-2xy+5xy-10y²-3xy` `⇒ x²-10y²=x²-10y²`(đpcm) Bình luận
Xét $VT$:
$(x+y)(x-y)-9y^2$
$=x^2-y^2-9y^2$
$=x^2-10y^2$ (1)
Xét $VP$:
$(x-2y)(x+5y)-3xy$
$=x(x+5y)-2y(x+5y)-3xy$
$=x^2+5xy-2xy-10y^2-3xy$
$=x^2+(5xy-2xy-3xy)-10y^2$
$=x^2-10y^2$ (2)
Từ (1), (2)
$→VT=VP$ (ĐPCM)
`(x+y)(x-y)-9y²=(x-2y)(x+5y)-3xy`
`⇒ x²-y²-9y²=x²-2xy+5xy-10y²-3xy`
`⇒ x²-10y²=x²-10y²`(đpcm)