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What is the greatest possible value of $a$ in the system of equations $5a + 2b = 0$ and $ab = -10$ ?

So ive currently done this:

ab=-10

a=-10/b

substitued into 5a+2b=0

to get

-50/b +2b = 0

multiplied b

-50 + 2b^2 = 0

2b^2 -50 = 0

Now im a little lost

Please help, please and thank you

 Dec 20, 2020

Best Answer 

 #3
avatar+117576 
+1

5a + 2b   = 0     (1)

ab  = -10   ⇒    b  =  -10/a   (2)

 

Put (2) into (1)  for   b   and we  have

 

5a +  2 ( -10/a)   = 0        

 

5a  -  20/a   =   0     multiply through by a

 

5a^2   -20    =   0      divide  through  by 5

 

a^2  - 4     =   0        factor as a difference  of  squares

 

(a - 2) ( a + 2)  =   0  

 

Setting each factor  to 0 and  solving  for a  produces  a  =  2     or  a   =  -2

 

a  = 2   is the  greatest  value  for a   

 

 

cool cool cool

 Dec 20, 2020
 #1
avatar
0

OK....see if this helps:

2b^2 -50 = 0

2b^2 = 50

b^2 = 25

b = +- 5        

 Dec 20, 2020
 #2
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0

So 5a+2b=0 and ab=-10. 

Then a = -10/b

Then substitute into 5a+2b= 0  to get 5(-10/b) +2b = 0 to get -50 +2b^2 = 0. 

Then 2b^2 = 50 

b^2 = 25

b = +5 and -5. 

5 is bigger than -5 so the answer is 5

 Dec 20, 2020
 #3
avatar+117576 
+1
Best Answer

5a + 2b   = 0     (1)

ab  = -10   ⇒    b  =  -10/a   (2)

 

Put (2) into (1)  for   b   and we  have

 

5a +  2 ( -10/a)   = 0        

 

5a  -  20/a   =   0     multiply through by a

 

5a^2   -20    =   0      divide  through  by 5

 

a^2  - 4     =   0        factor as a difference  of  squares

 

(a - 2) ( a + 2)  =   0  

 

Setting each factor  to 0 and  solving  for a  produces  a  =  2     or  a   =  -2

 

a  = 2   is the  greatest  value  for a   

 

 

cool cool cool

CPhill Dec 20, 2020

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