Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 127305 by MathSh last updated on 28/Dec/20

(a−3)^(−(1/5))   the set of possible values of a  a)(−∞;+∞)  b)(3;+∞)  e)a≠3

$$\left({a}−\mathrm{3}\right)^{−\frac{\mathrm{1}}{\mathrm{5}}} \\ $$$${the}\:{set}\:{of}\:{possible}\:{values}\:{of}\:{a} \\ $$$$\left.{a}\right)\left(−\infty;+\infty\right) \\ $$$$\left.{b}\right)\left(\mathrm{3};+\infty\right) \\ $$$$\left.{e}\right){a}\neq\mathrm{3} \\ $$

Answered by MJS_new last updated on 28/Dec/20

depending on the definition we use...  b=(1/( ((a−3))^(1/5) ))  (1) a∈R∧b∈R; (x)^(1/5) =sign x ((∣x∣))^(1/5)  (i.e. ((−32))^(1/5) =−2  ⇒ a≠3 ⇒ a∈R\{3}  (2) a∈C∧b∈C; (x)^(1/5) =∣x∣e^(i((arg x)/5))   ⇒ a≠3 ⇒ a∈C\{3}

$$\mathrm{depending}\:\mathrm{on}\:\mathrm{the}\:\mathrm{definition}\:\mathrm{we}\:\mathrm{use}... \\ $$$${b}=\frac{\mathrm{1}}{\:\sqrt[{\mathrm{5}}]{{a}−\mathrm{3}}} \\ $$$$\left(\mathrm{1}\right)\:{a}\in\mathbb{R}\wedge{b}\in\mathbb{R};\:\sqrt[{\mathrm{5}}]{{x}}=\mathrm{sign}\:{x}\:\sqrt[{\mathrm{5}}]{\mid{x}\mid}\:\left(\mathrm{i}.\mathrm{e}.\:\sqrt[{\mathrm{5}}]{−\mathrm{32}}=−\mathrm{2}\right. \\ $$$$\Rightarrow\:{a}\neq\mathrm{3}\:\Rightarrow\:{a}\in\mathbb{R}\backslash\left\{\mathrm{3}\right\} \\ $$$$\left(\mathrm{2}\right)\:{a}\in\mathbb{C}\wedge{b}\in\mathbb{C};\:\sqrt[{\mathrm{5}}]{{x}}=\mid{x}\mid\mathrm{e}^{\mathrm{i}\frac{\mathrm{arg}\:{x}}{\mathrm{5}}} \\ $$$$\Rightarrow\:{a}\neq\mathrm{3}\:\Rightarrow\:{a}\in\mathbb{C}\backslash\left\{\mathrm{3}\right\} \\ $$

Commented by MathSh last updated on 28/Dec/20

Thanks sir

$${Thanks}\:{sir} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com