Expert Answer to "Find two numbers whose sum is 10 and..."

jazzcutie0h

Answered question

2021-11-14

Find two numbers whose sum is 10 and product is -24 write the answer as integers or simplify fractions

Upout1940

Beginner2021-11-15Added 9 answers

Step 1
Let the two numbers be x and y

∴ x + y = 10

--(1)

x y = - 24

--(2)

y = \frac{- 24}{x}

substituting in (1)
Step 2

x - \frac{24}{x} = 10

x^{2} - 24 = 10 x

x^{2} - 10 x - 24 = 0

using quadratic formula,

x = \frac{x \pm \sqrt{100 - 4 (1) (- 24)}}{2 (1)}

x = \frac{10 \pm \sqrt{196}}{2} = \frac{10 \pm 14}{2}

x = \frac{10 + 14}{2}, \frac{10 - 14}{2}

x = 12, - 2

∴ y = \frac{- 24}{x}

y = \frac{- 24}{12}, \frac{- 24}{- 2}

y = - 2, 12

Step 3
Hence, the two numbers are -2 and 12.

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