find x^4 + 1/x^4 when x + 1/x = 3
Answers
Step-by-step explanation:
[math]x+\frac{1}{x}=3[/math]
Taking square on both sides
([math]x+\frac{1}{x})^2=3^2[/math]
[math]x^2+\frac{1}{x^2}+2=9[/math]
[math]x^2+\frac{1}{x^2}=9-2[/math]
[math]x^2+\frac{1}{x^2}=7[/math]
Again taking square on both sides, we have
[math](x^2+\frac{1}{x^2})^2=7^2[/math]
[math](x^2)^2+(\frac{1}{x^2})^2+2=49[/math]
[math]x^4+\frac{1}{x^4}=49-2[/math]
[math]x^4+\frac{1}{x^4}=47[/math][math]x+\frac{1}{x}=3[/math]
Taking square on both sides
([math]x+\frac{1}{x})^2=3^2[/math]
[math]x^2+\frac{1}{x^2}+2=9[/math]
[math]x^2+\frac{1}{x^2}=9-2[/math]
[math]x^2+\frac{1}{x^2}=7[/math]
Again taking square on both sides, we have
[math](x^2+\frac{1}{x^2})^2=7^2[/math]
[math](x^2)^2+(\frac{1}{x^2})^2+2=49[/math]
[math]x^4+\frac{1}{x^4}=49-2[/math]
[math]x^4+\frac{1}{x^4}=47[/math]