If $x^2 - 8x + 1 = 0$, what is the value of $x^8 - 3842x^4 + 1$ ? |
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We know that, If x + \(\frac{1}{x}\) = n then, x2 + \(\frac{1}{x^2}\) = \(\sqrt {n^2 - 2}\) If $x^2 - 8x + 1 = 0$, what is the value of $x^8 - 3842x^4 + 1$ = ? Here we can write $x^8 - 3842x^4 + 1$ as x4 + \(\frac{1}{x^4}\) - 3842 Divide on If $x^2 - 8x + 1 = 0$ both sides by x we get, x + \(\frac{1}{x}\) = 8 x2 + \(\frac{1}{x^2}\) = \(\sqrt {8^2 - 2}\) = 62 x4 + \(\frac{1}{x^4}\)= \(\sqrt {62^2 - 2}\) = 3842 Now put these above values in required equation, x4 + \(\frac{1}{x^4}\) - 3842 = 3842 - 3842 = 0 |