giải phương trình: $x^2 +$ $\frac{81x^2}{(x+9)^2}$ $=40$ 13/10/2021 Bởi Reagan giải phương trình: $x^2 +$ $\frac{81x^2}{(x+9)^2}$ $=40$
Đáp án: `thaipro` `x \ne -9` `x^2+(81x^2)/(x+9)^2=40` `⇔x^2(x+9)^2+81x^2=40(x+9)^2` `⇔x^2(x^2+18x+81)+81x^2=40(x^2+18x_81)` `⇔x^4+18x^3+81x^2+81x^2=40x^2+720x+3240` `⇔x^4+18x^3+122x^2-720x-3240=0` `⇔(x^4-2x^3-18x^2)+(20x^3-40x^2-360x)+(180x^2-360x-3240)=0` `⇔(x^2-2x-18)(x^2+20x+180)=0` `⇔`\(\left[ \begin{array}{l}x^2-2x-18=0\\x^2+20x+180=0\end{array} \right.\) `⇔`\(\left[ \begin{array}{l}x=1+\sqrt19\\x=1-\sqrt19\end{array} \right.\) Bình luận
Đáp án: Giải thích các bước giải: `x^2+\frac{81x^2}{(x+9)^2}=40` $⇔\dfrac{x^2(x+9)^2}{(x+9)^2}+\dfrac{81x^2}{(x+9)^2}=$ $\dfrac{40}{(x+9)^2}$ `⇒x^2(x^2+18x+81)+81x^2=40(x^2+18x+81)` `⇔x^4+18x^3+81x^2+81x^2=40x^2+720x+3240` `⇔x^4+18x^3+162x^2-40x^2-720x-3240=0` `⇔x^4+18x^3+122x^2-720x-3240=0` `⇔`\(\left[ \begin{array}{l}x=1-\sqrt 19\\x=\sqrt 19 +1\end{array} \right.\) Vậy.. Bình luận
Đáp án:
`thaipro`
`x \ne -9`
`x^2+(81x^2)/(x+9)^2=40`
`⇔x^2(x+9)^2+81x^2=40(x+9)^2`
`⇔x^2(x^2+18x+81)+81x^2=40(x^2+18x_81)`
`⇔x^4+18x^3+81x^2+81x^2=40x^2+720x+3240`
`⇔x^4+18x^3+122x^2-720x-3240=0`
`⇔(x^4-2x^3-18x^2)+(20x^3-40x^2-360x)+(180x^2-360x-3240)=0`
`⇔(x^2-2x-18)(x^2+20x+180)=0`
`⇔`\(\left[ \begin{array}{l}x^2-2x-18=0\\x^2+20x+180=0\end{array} \right.\)
`⇔`\(\left[ \begin{array}{l}x=1+\sqrt19\\x=1-\sqrt19\end{array} \right.\)
Đáp án:
Giải thích các bước giải:
`x^2+\frac{81x^2}{(x+9)^2}=40`
$⇔\dfrac{x^2(x+9)^2}{(x+9)^2}+\dfrac{81x^2}{(x+9)^2}=$ $\dfrac{40}{(x+9)^2}$
`⇒x^2(x^2+18x+81)+81x^2=40(x^2+18x+81)`
`⇔x^4+18x^3+81x^2+81x^2=40x^2+720x+3240`
`⇔x^4+18x^3+162x^2-40x^2-720x-3240=0`
`⇔x^4+18x^3+122x^2-720x-3240=0`
`⇔`\(\left[ \begin{array}{l}x=1-\sqrt 19\\x=\sqrt 19 +1\end{array} \right.\)
Vậy..