SOLUTION: The sum of a number and twice its reciprical is 3. Fing the number.

Question 129669This question is from textbook Algebra structure and meathod
: The sum of a number and twice its reciprical is 3. Fing the number. This question is from textbook Algebra structure and meathod

Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
If the number is x, then it's reciprocal is 1/x. So the sum of the number and twice its reciprocal is x+2(1/x), or x+(2/x). So x+(2/x)=3. In order to find the sum, we need a common denominator. The denominator of x is 1, so we could use the common denominator of x. x then becomes (x^2)/x, so we have ((x^2)/x)+(2/x)=3. Add the numerators to get (x^2+2)/x=3. Cross multiply to get x^2+2=3x. Now you have a quadratic equation, x^2-3x+2=0. Factor this to (x-2)(x-1)=0, so x=2 or x=1. If you check these, they both work.
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