Question

Find 2 numbers whose sum is 23 and product is 120.

Answer 1

Step-by-step explanation:

Let the numbers be x and y

x+y=23

xy=120

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy$

${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ {(x - y)}^{2} = {(x + y)}^{2} - 2xy - 2xy \\ {(x - y)}^{2} = {(x + y)}^{2} - 4xy \\ {(x - y)}^{2} = {23}^{2} - 4 \times 120 = 529 - 480 \\ {(x - y)}^{2} = 49 \\ x - y = 7$

x+y=23………….…(i)

x-y=7……………….(ii)

(i)+(ii)

2x=30

x=15

y=23-x=23-15=8

$<font color=red><marquee>The answer is 15 and 8</marquee></font>$

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