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Bas_tet [7]
1 year ago
14

Find all complex solutions of the equation 2^2 − 6 + 49 = 0. Express complex numbers in the form + .

Mathematics
1 answer:
Vladimir [108]1 year ago
6 0

To find the complex solutions of the equation we use the quadratic formula:

\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4(2)(49)}}{2(2)} \\ =\frac{6\pm\sqrt[]{36-392}}{4} \\ =\frac{6\pm\sqrt[]{-356}}{4} \\ =\frac{6\pm i\sqrt[]{356}}{4} \\ =\frac{6\pm i\sqrt[]{4\cdot89}}{4} \\ =\frac{6\pm i2\sqrt[]{89}}{4} \\ =\frac{3\pm i\sqrt[]{89}}{2} \end{gathered}

Therefore the solutions of the equation are:

\begin{gathered} x=\frac{3}{2}+\frac{\sqrt[]{89}}{2}i \\ \text{ or } \\ x=\frac{3}{2}-\frac{\sqrt[]{89}}{2}i \end{gathered}

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Step-by-step explanation:

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Step 1; Adam earns a basic pay of £200 each week. He earns 10% of the magazine price for each sold  and 15% of the book price for each sold. Each magazine costs £8 and each book costs £15. He sells 42 magazines and 14 books.

Money earned for selling a magazine = 10% × £8 = 0.10 × £8 = £0.80,

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Money earned for selling 42 magazines and 14 books = £33.60 + £31.50 =  £65.10.

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Last week's salary =  £200 +  £65.10 = £265.10.

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