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2. The product of two consecutive odd numbers is 143. Find the numbers. (Hint: If the first odd number is x, what is the next odd number?)​

User CoMartel
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1 Answer

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Explanation:

we have the 2 numbers x and (x+2).

x × (x + 2) = 143

x² + 2x = 143

x² + 2x - 143 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case this is

x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =

= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =

= (-2 ± 24)/2 = (-1 ± 12)

x1 = -1 + 12 = 11

x2 = -1 - 12 = -13

so, we have 2 solutions : 11 and 13, -13 and -11

11× 13 = 143

-11×-13 = 143

User NilsB
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