Multiple choice

Find the roots of the following equation: $\displaystyle\,35y^2\,+\,\frac{12}{y^2}\,=\,44$, then

  1. $\displaystyle\,y\,=\,\pm\,\sqrt\frac{6}{7},\,\,\pm\,\sqrt\frac{2}{5}$
  2. $\displaystyle\,y\,=\,\pm\,\sqrt\frac{6}{11},\,\,\pm\,\sqrt\frac{2}{5}$
  3. $\displaystyle\,y\,=\,\pm\,\sqrt\frac{6}{7},\,\,\pm\,\sqrt\frac{2}{7}$
  4. $\displaystyle\,y\,=\,\pm\,\sqrt\frac{6}{7},\,\,\pm\,\sqrt\frac{3}{5}$
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A Correct answer
Explanation

Let u = y^2. The equation is 35u + 12/u = 44. Multiply by u: 35u^2 - 44u + 12 = 0. Using the quadratic formula, u = (44 +/- sqrt(1936 - 1680)) / 70 = (44 +/- 16) / 70. u1 = 60/70 = 6/7, u2 = 28/70 = 2/5. Thus y = +/- sqrt(6/7) and +/- sqrt(2/5).