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Question 53161: A NUMBER IS 21/10 MORE THAN ITS RECIPROCAL. FIND THE NUMBER.
DOMAIN (2/5, 3/5, 5/4, 5/2)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A NUMBER IS 21/10 MORE THAN ITS RECIPROCAL. FIND THE NUMBER.
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21/10 can easily be handled as decimal; 2.1, so we can write it:
x = 1/x + 2.1
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Mult equation by x to get rid of the denominator, you have:
x^2 = 1 + 2.1x
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x^2 - 2.1x - 1 = 0 arranged as a quadratic equation
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Solve for x your favorite method and you get
x = +2.5, x = -.4
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if you prefer fractions:
x = 5/2, x = -4/10
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Check with x = 2.5
2.5 = (1/2.5) + 2.1
2.5 = .5 + 2.1
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Check with x = -.4
-.4 = (1/-.4) + 2.1
-.4 = -2.5 + 2.1
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