Final answer:
To find two consecutive numbers whose product is 19, set up the equation x(x+1) = 19 and solve using the quadratic formula. The numbers are approximately 3 and 4.
Step-by-step explanation:
To find two consecutive numbers whose product is 19, we can set up the equation:
x(x+1) = 19
Expanding the equation, we get:
x^2 + x = 19
Rewriting the equation in standard form, we have:
x^2 + x - 19 = 0
Using the quadratic formula, we can solve for x:
x = (-1 ± sqrt(1^2 - 4*1*(-19))) / 2*1
Calculating the values, we get x ≈ 3.15 and x ≈ -4.15. Since we are looking for consecutive numbers, the solution is x ≈ 3 and x ≈ 4.
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