Задача 67391 Help me. №5...

638f7346ddba6d42a21cccd5

06.12.2022 19:55:31

Help me. №5

5f3ea7e3faf909182968ddd9

06.12.2022 20:28:39

★

[m]\left\{\begin {matrix}x^7\cdot y^9=a\\x^3\cdot y^4=b\end {matrix}\right.[/m]

a ≠ 0; b ≠ 0

[m]\left\{\begin {matrix}x^7\cdot y^9=a\\ y^4=\frac{b}{x^3}\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}x^7\cdot y^4\cdot y^4\cdot y=a\\ y=\sqrt[4]{\frac{b}{x^3}}\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}x^7\cdot \frac{b}{x^3}\cdot \frac{b}{x^3}\cdot \sqrt[4]{\frac{b}{x^3}}=a\\ y=\sqrt[4]{\frac{b}{x^3}}\end {matrix}\right.[/m] ⇒


[m]\left\{\begin {matrix}x\cdot b^2\cdot \sqrt[4]{\frac{b}{x^3}}=a\\ y=\sqrt[4]{\frac{b}{x^3}}\end {matrix}\right.[/m]

возводим первое в четвертую степень

[m]\left\{\begin {matrix}x^4\cdot b^8\cdot \frac{b}{x^3}=a^4\\ y=\sqrt[4]{\frac{b}{x^3}}\end {matrix}\right.[/m]


[m]\left\{\begin {matrix}x\cdot b^9=a^4\\ y=\sqrt[4]{\frac{b}{x^3}}\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}x=\frac{a^4}{b^9}\\ y=\sqrt[4]{\frac{b}{x^3}}\end {matrix}\right.[/m] ⇒ [m]x^3=\frac{a^{12}}{b^{27}}[/m]

[m]\left\{\begin {matrix}x=\frac{a^4}{b^9} \\ y=\sqrt[4]{\frac{b}{\frac{a^{12}}{b^{27}}}}\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}x=\frac{a^4}{b^9} \\ y=\sqrt[4]{\frac{b^{28}}{a^{12}}}\end {matrix}\right.[/m] ⇒

[m]\left\{\begin {matrix}x=\frac{a^4}{b^9} \\ y=\frac{b^7}{a^3}\end {matrix}\right.[/m]