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juin [17]
2 years ago
10

Solve each equation. Identify the solutions as rational or irrational numbers.

Mathematics
1 answer:
Fiesta28 [93]2 years ago
6 0

\textbf{a)}\\\\~~~~~~~x(3x-4)=5\\\\\implies 3x^2 -4x = 5\\\\\implies 3x^2 -4x=5\\\\\implies x^2 - \dfrac 43 x = \dfrac 53\\ \\\implies x^2 - 2\cdot \dfrac 23 \cdot x + \left( \dfrac 23 \right)^2 - \left( \dfrac 23 \right)^2 =  \dfrac 53\\\\\implies \left(x-\dfrac  23 \right)^2 = \dfrac 53 + \dfrac 49\\\\\implies \left(x-\dfrac  23 \right)^2= \dfrac{19}{9}\\\\\implies x- \dfrac 23 =  \pm\dfrac{\sqrt{19}}3\\\\\implies x=\dfrac 23 \pm\dfrac{\sqrt{19}}3\\\\

\text{The solutions are irrational.}\\\\\\\textbf{b)}\\\\~~~~~~~(3x-2)^2 = \dfrac 14\\\\\implies 3x -2 = \pm \dfrac 12\\\\\implies  3x = 2\pm  \dfrac 12\\\\\implies x = \dfrac 23 \pm \dfrac 16\\\\ \implies x = \dfrac 56 ,~~ x =\dfrac 12 \\ \\\text{The solutions are  rational .}

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