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The operation $*$ is defined for non-zero integers as follows: $a * b = \frac{1}{a} + \frac{1}{b}$. If $a+b = 9$ and $ a \times b = 20$, what is the value of $a*b$? Express your answer as a common fraction.

 Nov 11, 2014

Best Answer 

 #2
avatar+128570 
+5

a + b = 9   →  b = 9  -a

a*b = 20   →  a(9 - a) = 20  → -a2 + 9a = 20 →   a2 - 9a + 20 = 0   and factoring, we have (a - 5) (a - 4) = 0

So  a  = 4 or 5    ....either way, we will be adding the fractions

1/4 + 1/5   =  9 / 20  = .45

 

 Nov 11, 2014
 #1
avatar+14 
+5

$$a*b =\frac{1}{a} + \frac{1}{b}

Hence:

a*b = (a+b)/(a x b)

a+b = 9 , a x b = 20

a*b = 0.45$$

.
 Nov 11, 2014
 #2
avatar+128570 
+5
Best Answer

a + b = 9   →  b = 9  -a

a*b = 20   →  a(9 - a) = 20  → -a2 + 9a = 20 →   a2 - 9a + 20 = 0   and factoring, we have (a - 5) (a - 4) = 0

So  a  = 4 or 5    ....either way, we will be adding the fractions

1/4 + 1/5   =  9 / 20  = .45

 

CPhill Nov 11, 2014

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