Question

if X + 1 by X equal to 5 find the value of x power 4 + 1 by x power 4​

Answer 1

                   

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$\huge\boxed{\ \ \ \ \ \huge\boxed{\ \ \ \ \ \huge\boxed{\ \ \ \ \ \bold{ANSWER:\ 527}\ \ \ \ \ }\ \ \ \ \ }\ \ \ \ \ }$

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$x+\frac{1}{x}=5 \\ \\ \\ (x+\frac{1}{x})^2=5^2 \\ \\ \Rightarrow\ x^2 + \frac{1}{x^2} + (2 \times x \times \frac{1}{x})=25 \\ \\ \Rightarrow\ x^2+\frac{1}{x^2}+2=25 \\ \\ \Rightarrow\ x^2+\frac{1}{x^2}=23 \\ \\ \\ (x^2+\frac{1}{x^2})^2=23^2 \\ \\ x^4+\frac{1}{x^4}+(2 \times x^2 \times \frac{1}{x^2})=529 \\ \\ x^4+\frac{1}{x^4}+2=529 \\ \\ x^4+\frac{1}{x^4}=\bold{527}$

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$\huge\boxed{\ \ \ \ \ \huge\boxed{\ \ \ \ \ \bold{TO\ REMEMBER...}\ \ \ \ \ }\ \ \ \ \ }$

$\sf{If} \ \ x+\frac{1}{x}=k, \\ \\ \\ \sf{then} \ \\ \\ \\ x^4+\frac{1}{x^4}=(k-2-\sqrt{2})(k-2+\sqrt{2})$

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$\sf{Here,} \ \\ \\ \\ x^4+\frac{1}{x^4}=(5^2-2-\sqrt{2})(5^2-2+\sqrt{2}) \\ \\ \Rightarrow\ x^4+\frac{1}{x^4}=(25-2-\sqrt{2})(25-2+\sqrt{2}) \\ \\ \Rightarrow\ x^4+\frac{1}{x^4}=(23-\sqrt{2})(23+\sqrt{2}) \\ \\ \Rightarrow\ x^4+\frac{1}{x^4}=23^2-(\sqrt{2})^2 \\ \\ \Rightarrow\ x^4+\frac{1}{x^4}=529-2 \\ \\ \Rightarrow\ x^4+\frac{1}{x^4}=\bold{527}$

$\sf{Plz mark it as the brainliest. \\ \\ \\ Thank you. :-))}$

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