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77julia77 [94]
10 months ago
12

in Each diagram below right, the 2 numbers on the side of the x that are multiplied together to get the top number of the x but

added together to get the bottom number of the x

Mathematics
1 answer:
lakkis [162]10 months ago
7 0

We need to satisfy the following equations:

x*y = 13

x + y = -14

Isolating x from the first equation,

x = -14 - y

Substituting this result into the first equation,

(-14 - y)*y = 13

-14y- y*y = 13

-y² - 14y - 13 = 0

Using the quadratic formula,

\begin{gathered} y_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y_{1,2}=\frac{14\pm\sqrt[]{(-14)^2-4\cdot(-1)\cdot(-13)}}{2\cdot(-1)} \\ y_{1,2}=\frac{14\pm\sqrt[]{144}}{-2} \\ y_1=\frac{14+12}{-2}=-13 \\ y_2=\frac{14-12}{-2}=-1 \end{gathered}

Therefore, the solution is:

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