Practicing Success
If $20x^{2} — 30x + 1 = 0$, then what is the value of $25x^{2}+\frac{1}{16x^{2}}$ |
58$\frac{3}{4}$ 53$\frac{3}{4}$ 53$\frac{1}{2}$ 58$\frac{1}{2}$ |
53$\frac{3}{4}$ |
If $K+\frac{1}{K}=n$ then, $K^2+\frac{1}{K^2}$ = n2 – 2 × k × \(\frac{1}{k}\) If $20x^{2} — 30x + 1 = 0$, then what is the value of $25x^{2}+\frac{1}{16x^{2}}$ Divide $20x^{2} — 30x + 1 = 0$ by 5x on both sides to get the desired format of the equation, 5x + \(\frac{1}{4x^2}\) = \(\frac{30}{4}\) = \(\frac{15}{2}\) So, $25x^{2}+\frac{1}{16x^{2}}$ = ( \(\frac{15}{2}\) )2 – 2 × 5x × \(\frac{1}{4x}\) $25x^{2}+\frac{1}{16x^{2}}$ = \(\frac{225}{4}\) - \(\frac{5}{2}\) $25x^{2}+\frac{1}{16x^{2}}$ = \(\frac{225 - 10}{4}\) = \(\frac{215}{4}\) $25x^{2}+\frac{1}{16x^{2}}$ = 53$\frac{3}{4}$ |