SOLUTION: the product of two number is 1 the sum of the large number and the twice the smaller number is 11 find the two numbers

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Question 1122999: the product of two number is 1 the sum of the large number and the twice the smaller number is 11 find the two numbers
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Adjusted:
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The product of two numbers is 1.
The sum of the large number and twice the smaller number is 11.
Find the two numbers.
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Two numbers, x and 1/x.

x%2A%281%2Fx%29=1

second part of description gives
highlight_green%28x%2B2%2Fx=11%29
Solve this.

x%5E2%2B2=11x
x%5E2-11x%2B2=0
x=%2811%2B-+sqrt%28121-4%2A2%29%29%2F2
highlight%28x=%2811%2B-+sqrt%28113%29%29%2F2%29

x is either 0.184927 or 10.81507
(They both work)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!






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You need to check both of these answers. Since we introduced a squared term in the process of solving the problem, there is the potential that we introduced an extraneous root. Hence, you either have 2, 1, or 0 answers to the problem. I'll leave it to you to figure out which is correct. Remember when you check these numbers in the second equation that is presumed to be the larger of itself and its reciprocal.


John

My calculator said it, I believe it, that settles it