If the roots of the following quadratic equat | vedclass

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Question

(A) Given equation: $x + \frac{2}{x} - 8 = 0$. Multiply the entire equation by $x$ to get: $x^2 - 8x + 2 = 0$. To solve by completing the square,we re

Vedclass · Accepted Answer

$4 + \sqrt{14}, 4 - \sqrt{14}$

Vedclass · Answer

(A) Given equation: $x + \frac{2}{x} - 8 = 0$. Multiply the entire equation by $x$ to get: $x^2 - 8x + 2 = 0$. To solve by completing the square,we rewrite the equation as: $x^2 - 8x = -2$. Add the square of half the coefficient of $x$ to both sides. The coefficient of $x$ is $-8$,so half of it is $-4$,and its square is $(-4)^2 = 16$. Adding $16$ to both sides: $x^2 - 8x + 16 = -2 + 16$. This simplifies to: $(x - 4)^2 = 14$. Taking the square root on both sides: $x - 4 = \pm \sqrt{14}$. Therefore,$x = 4 \pm \sqrt{14}$. The roots are $4 + \sqrt{14}$ and $4 - \sqrt{14}$.

If the roots of the following quadratic equation exist,find them by the method of completing the square: $x + \frac{2}{x} - 8 = 0$.

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