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put this solution on YOUR website!The sum of a number and twice its reciprocal is 3
Review:
sum means to add
twice: 2 times something
reciprocal: a number flipped over. For example the reciprocal of 3 is (1/3)
let n stand for the words "a number"
then its reciprocal would be (1/n)
Therefore your expression would be:
n + 2*(1/n) = 3
n + (2/n) = 3 --> 2*(1/n) would be the same as 2/n
We need to get the n out of the denominator, so multiply EVERY term by n
which would give you:
n*n + 2 = 3*n --> n * n = n^2
n^2 + 2 = 3n --> subtract the 3n across to the other side
n^2 - 3n + 2 = 0 --> factor into two binomials
( n - 2) (n - 1) = 0 --> set each equal to 0
n - 2 = 0 and n - 1 = 0,
so when you solve n = 2 and n = 1
Check both solutions:
if n=2
2 + 2/2 = 3 which is true because when you solve 2+1 = 3
if n= 1
1 + 2/1 = 3 which is also true: 1 + 2 = 3
So the solutions are 1 and 2.
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