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Question Number 143208 by Gbenga last updated on 11/Jun/21

$$3^x+4x-3=x^4$$$$findx$$

Answered by MJS_new last updated on 11/Jun/21

$$\mathrm{you}\mathrm{can}\mathrm{only}\mathrm{approximate}$$$$3^x=x^4-4x+3$$$$f\left(x\right)=3^x\mathrm{is}\mathrm{strictly}\mathrm{increasing}\mathrm{\forall }x\in \mathbb{R}$$$$g\left(x\right)=x^4-4x+3\mathrm{has}\mathrm{an}\mathrm{absolute}\mathrm{minimum}$$$$\mathrm{at}\left(\begin{array}{c}1\\ 0\end{array}\right)\mathrm{and}\mathrm{is}\mathrm{strictly}\mathrm{decreasing}\mathrm{for}x<1$$$$\mathrm{and}\mathrm{strictly}\mathrm{increasing}\mathrm{for}x>1$$$$f\left(0\right)=1\wedge g\left(0\right)=3\Rightarrow \mathrm{we}\mathrm{have}\mathrm{to}\mathrm{search}\mathrm{for}x>0$$$$f\left(8\right)=6561\wedge g\left(8\right)=4067\Rightarrow x<8$$$$\mathrm{I}\mathrm{get}$$$$x_1\approx .376830$$$$x_2\approx 1.87395$$$$x_3\approx 7.15659$$

Commented by Gbenga last updated on 11/Jun/21

$$thanks$$

Commented by Gbenga last updated on 11/Jun/21

$$findxinx+e^x+x^4-4=0$$

Commented by mr W last updated on 11/Jun/21

$$thereisnostandardexactwayfor$$$$solution!thereforemoresuch$$$$questionsmakenosense.$$$$youmayaskasnext$$$$findxinx+e^{-x}+x^4-4=0$$$$findxinx+\sin x+x^4-4=0$$$$findxinx+\cosh x+x^4-4=0$$$$......$$

Commented by Gbenga last updated on 12/Jun/21

$$0ksir$$

Commented by Gbenga last updated on 12/Jun/21

$$butitwasalsosenttomebyafriend$$

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