Cho tỉ lệ thức $\frac{a}{b}$ = $\frac{c}{d}$. Chứng minh rằng: $\frac{2019a^{2}+2020b^{2}}{2019a^{2}-2020b^{2}$}$ =
$\frac{2019c^{2}+2020d^{2}}{2019c^{2}-2020d^{2}$}$
Cho tỉ lệ thức $\frac{a}{b}$ = $\frac{c}{d}$. Chứng minh rằng: $\frac{2019a^{2}+2020b^{2}}{2019a^{2}-2020b^{2}$}$ = $\frac{2019c^{2}+2020d^{2}}{2019c
By Abigail
Đáp án:
`a/b=c/d`
`-> a/c=b/d`
`-> (2019a^2)/(2019c^2)=(2020b^2)/(2020d^2)`
`=(2019a^2+2020b^2)/(2019c^2+2020d^2)“=(2019a^2-2020b^2)/(2019c^2-2020d^2)`
`-> (2019a^2+2020b^2)/(2020a^2-2020b^2)=(2019c^2+2020d^2)/(2019c^2-2020d^2)`
`-> đpcm`
`VT=a/b=c/d↔a/c=b/d`
`↔(2019a^2)/(2019c^2)=(2020b^2)/(2020d^2)`
`↔(2019a^2+2020b^2)/(2019a^2+2020d^2)=(2019a^2-2020b^2)/(2019c^2-2020d^2)`
`↔(2019a^2+2020b^2)/(2020a^2-2020b^2)=(2019c^2+2020d^2)/(2019c^2-2020d^2)=VP`
Vậy `(2019a^2+2020b^2)/(2020a^2-2020b^2)=(2019c^2+2020d^2)/(2019c^2-2020d^2)`