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Attempt following question by selecting a choice to answer. c Find two numbers whose difference is 22 and their product is minimum.

fff ccc A.

c 12, - 10

B.

c 11, - 11

C.

c 9, - 13

D.

c - 14, 8

cc
B

Step 1: Let x represents one number. Step 2: Let 22 + x represents the other number.[Since the difference is 22.] Step 3: Let y represents the product of the two numbers. Step 4: y = x (22 + x )[Express as an equation.] Step 5: y = x ^{2} + 22x [Multiply.] Step 6: y = x ^{2} + 22x is a quadratic with a = 1 and b = 22.[Compare with y = ax ^{2} + bx + c .] Step 7: a = 1 > 0. So, the parabola opens upward with its vertex being the minimum point. Step 8: This minimum point occurs when x = - b 2 a . Step 9: x = - 22 2(1) = - 11[Substitute and simplify.] Step 10: If x = - 11, then 22 + x = 22 + (- 11) = 11. Step 11: So, the numbers are 11 and - 11.