4p^2 12 p + 7 = 0 p = 12±√((12)^2 4 × 4× 7)2×4 = 12±√(144 112)8 = 12±4√(2)8 p_1 = 3+√(2)2 p_2 = 3 √(2)2 ...

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Addition of Fractions

Solve 4p2+7...

Question

Solve $4 p^{2} + 7 = 12 p$

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Solution

$4 p^{2} - 12 p + 7 = 0$

$p = \frac{12 \begin{matrix} \pm \end{matrix} \sqrt{(12)^{2} - 4 \times 4 \times 7}}{2 \times 4} = \frac{12 \begin{matrix} \pm \end{matrix} \sqrt{144 - 112}}{8} = \frac{12 \begin{matrix} \pm \end{matrix} 4 \sqrt{2}}{8}$

$p_{1} = \frac{3 + \sqrt{2}}{2} p_{2} = \frac{3 - \sqrt{2}}{2}$

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