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# help

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If x + 1/x = 3, then find x^4 + 1/x^4.

Jun 17, 2020

#1
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Instead of trying to figure out the value of x, we can use clever squaring.

Square the first equation.

$$(x+\frac{1}{x})^2= 3^2$$

$$x^2+1+1+\frac{1}{x^2}=9$$

$$x^2+\frac{1}{x^2}=7$$

Square this equation again.

$$(x^2+\frac{1}{x^2})^2=7^2$$

$$x^4+1+1+\frac{1}{x^4}=49$$

$$x^4+\frac{1}{x^4}=47$$

Jun 17, 2020