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Question Number 78683 by berket last updated on 19/Jan/20

$$solve{x}^4-18x-35=0byusingsubstitutionx=u+v$$

Commented by john santu last updated on 20/Jan/20

$$x=u+v\Rightarrow x^3=u^3+v^3+3uv(u+v)$$$$x^4-18x-35=0$$$$x(x^3-18)-35=0$$$$x(u^3+v^3+3uvx-18)-35=0$$$$3uv{x}^2+(u^3+v^3-18)x-35=0$$$$$$$$$$

Commented by MJS last updated on 20/Jan/20

$$x^4?$$

Commented by john santu last updated on 20/Jan/20

$$x=\frac{18-(u^3+v^3)\pm \sqrt{{(u^3+v^3-18)}^2+420uv}}{6uv}$$$$hihihi...i{don}^{\prime }tknow$$

Commented by MJS last updated on 20/Jan/20

$$\mathrm{this}\mathrm{is}\mathrm{no}\mathrm{solution}\mathrm{as}\mathrm{you}\mathrm{know}...$$$$x=u+v\mathrm{leads}\mathrm{to}{\mathrm{Cardano}}^{\prime }\mathrm{s}\mathrm{solution}\mathrm{for}$$$$x^3+px+q=0$$$$\mathrm{in}\mathrm{this}\mathrm{case},\mathrm{for}{x}^3...\mathrm{one}\mathrm{solution}\mathrm{is}x=5,\mathrm{so}$$$$\mathrm{I}\mathrm{think}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{typo}$$

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