Question 115

If $$x^{2}+\frac{1}{x^2}=66$$ then the value of $$\frac{x^2-1+2x}{x}=$$ ?

Solution

Expression : $$x^{2}+\frac{1}{x^2}=66$$

=> $$(x - \frac{1}{x})^2 + 2 = 66$$

=> $$(x - \frac{1}{x})^2 = 64$$

=> $$x - \frac{1}{x} = \pm 8$$

To find : $$\frac{x^2-1+2x}{x}$$

= $$x - \frac{1}{x} + 2$$

= $$(8 + 2)$$ and $$(-8 + 2)$$

= 10 and -6

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