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What 2 numbers when multiplied together equal 10 but when added together equal 5?
Wiki User
∙ 12y ago
Let the two numbers be represented by a and b.
a x b = 10 ....so b = 10/a
and a + b = 5.... now substitute the above value for b
a + 10/a = 5 .... multiply throughout by a
a2 + 10 = 5a......re-arranging
a² - 5a + 10 = 0
When this quadratic equation is solved (by using the quadratic formula or completing the square) then a = 2.5 + 0.5i√15 and b = 2.5 - 0.5i√15
Check : a + b = 2.5 + 0.5i√15 + 2.5 - 0.5i√15 = 2.5 + 2.5 = 5
a x b = (2.5 + 0.5i√15)(2.5 - 0.5i√15) = 6.25 - 0.25i²*15 = 6.25 + 3.75 = 10
Wiki User
∙ 12y ago
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