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what two sum number equal to 7.5 and product of 9

 Sep 2, 2014

Best Answer 

 #2
avatar+128053 
+8

Nice answer Aziz....let's see how he might have gotten there......

Let x be the first number and y be the second  ...   so we have

x + y = 7.5

and

x * y = 9

Solving for y in the first equation, we have   y = 7.5 - x

And substitutuing for y in the second equation

x * (7.5 - x) = 9    simplifying, we have

-x^2 + 7.5 x   = 9      and rearranging, we have

x^2 - 7.5x + 9 = 0  subtract 9 from both sides

x^2 - 7.5x =  -9       now, take 1/2 of the coefficient on x (= 3.75), square it (=14.0625) , and add the square to both sides...so we have

x^2 - 7.5x + 14.0625 = 5.0625     factor the left side

(x - 3.75)^2  = 5.0625         take the square root of both sides

x - 3.75  = ± 2.25

So x = 3.75 - 2.25 = 1.5    or x = 3.75 + 2.25  = 6

And whatever we choose as x, y is the other value, so Aziz's answer of 1.5 and 6 is correct!!!!

 

 Sep 2, 2014
 #1
avatar+4473 
+8

1.5 & 6.

 

1.5 + 6 = 7.5

 

1.5*6 = 9.

 Sep 2, 2014
 #2
avatar+128053 
+8
Best Answer

Nice answer Aziz....let's see how he might have gotten there......

Let x be the first number and y be the second  ...   so we have

x + y = 7.5

and

x * y = 9

Solving for y in the first equation, we have   y = 7.5 - x

And substitutuing for y in the second equation

x * (7.5 - x) = 9    simplifying, we have

-x^2 + 7.5 x   = 9      and rearranging, we have

x^2 - 7.5x + 9 = 0  subtract 9 from both sides

x^2 - 7.5x =  -9       now, take 1/2 of the coefficient on x (= 3.75), square it (=14.0625) , and add the square to both sides...so we have

x^2 - 7.5x + 14.0625 = 5.0625     factor the left side

(x - 3.75)^2  = 5.0625         take the square root of both sides

x - 3.75  = ± 2.25

So x = 3.75 - 2.25 = 1.5    or x = 3.75 + 2.25  = 6

And whatever we choose as x, y is the other value, so Aziz's answer of 1.5 and 6 is correct!!!!

 

CPhill Sep 2, 2014

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