Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 89653 by student work last updated on 18/Apr/20

Commented by john santu last updated on 18/Apr/20

$$2^x=p\Rightarrow p^3+p=16$$$$useCardanomethod$$

Commented by student work last updated on 18/Apr/20

$$solveforme$$

Commented by student work last updated on 18/Apr/20

$$canudescibeformethecardanomethood?$$

Commented by MJS last updated on 18/Apr/20

$$\mathrm{you}\mathrm{can}\mathrm{search}\mathrm{on}\mathrm{google}$$$$\mathrm{if}\mathrm{you}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{know}\mathrm{how}\mathrm{to}\mathrm{solve}\mathrm{polynomes}$$$$\mathrm{of}{3}^{\mathrm{rd}}\mathrm{degree}\mathrm{you}\mathrm{will}\mathrm{have}\mathrm{to}\mathrm{study}\mathrm{for}\mathrm{a}\mathrm{while}$$

Answered by MJS last updated on 18/Apr/20

$$2^{3x}+2^x-16=0$$$$z=2^x\iff x=\frac{\ln z}{\ln 2}$$$$z^3+z-16=0\Rightarrow p=1\wedge q=-16$$$$D=\frac{p^3}{27}+\frac{q^2}{4}=\frac{1729}{27}>0\Rightarrow {\mathrm{Cardano}}^{\prime }\mathrm{s}\mathrm{Method}$$$$z_1=\sqrt[3]{8+\frac{\sqrt{5187}}{9}}-\sqrt[3]{-8+\frac{\sqrt{5187}}{9}}$$$$z_2\wedge z_3\notin \mathbb{R}$$$$\Rightarrow x=\frac{\ln (\sqrt[3]{8+\frac{\sqrt{5187}}{9}}-\sqrt[3]{-8+\frac{\sqrt{5187}}{9}})}{\ln 2}$$

Commented by mr W last updated on 18/Apr/20

$$toavoidmisunderstanding:$$$$\Rightarrow x=\frac{\ln (\sqrt[3]{8+\frac{\sqrt{5187}}{9}}-\sqrt[3]{-8+\frac{\sqrt{5187}}{9}})}{\ln 2}$$

Commented by MJS last updated on 18/Apr/20

$$\mathrm{thank}\mathrm{you}...$$$$\mathrm{btw}:\mathrm{is}\mathrm{it}\mathrm{a}\mathrm{typo}\mathrm{to}\mathrm{not}\mathrm{type}?$$

Commented by I want to learn more last updated on 18/Apr/20

$$\mathrm{I}\mathrm{think}\mathrm{because}\mathrm{the}\ln \mathrm{will}\mathrm{not}\mathrm{affect}\mathrm{everything}\mathrm{at}\mathrm{the}\mathrm{numerator}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com