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Let the two numbers be a and b. Then,
ab = 72 therefore b = 72/a. Substituting for b in a + b = -19 gives,
a + 72/a = -19 : multiply both sides by a.
a2 + 72 = -19a : therefore a2 + 19a + 72 = 0
Solving for a quadratic equation gives,
a = [-19 ± √(361 - 288)] ÷ 2 which simplifies to a = -9.5 ± 4.272 (3dp)
The two numbers are therefore -9.5 + 4.272 = -5.228 and -9.5 - 4.272 = -13.772
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∙ 14y ago
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