Practicing Success
If $x^{2}- 5x + 1 = 0$, then the value of $\left(x^{4} + \frac{1}{x^{2}}\right) \div (x^{2} + 1)$ is: |
21 22 25 24 |
22 |
If x + \(\frac{1}{x}\) = n then, $x^3 +\frac{1}{x^3}$ = n3 - 3 × n If $x^{2}- 5x + 1 = 0$ then the value of $\left(x^{4} + \frac{1}{x^{2}}\right) \div (x^{2} + 1)$ = ? we can write $\left(x^{4} + \frac{1}{x^{2}}\right) \div (x^{2} + 1)$ by taking x as common form numerator and denominator as = $\left(x^{3} + \frac{1}{x^{3}}\right) \div (x + \frac{1}{x})$ $x^{2}- 5x + 1 = 0$ Divide by x on both sides, x + \(\frac{1}{x}\) = 5 then, $x^3 +\frac{1}{x^3}$ = 53 - 3 × 5 = 110 So the value of $\left(x^{3} + \frac{1}{x^{3}}\right) \div (x + \frac{1}{x})$ = \(\frac{110}{5}\) = 22 |