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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

Dec 20, 2020

#3
+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

Dec 20, 2020

#1
0

OK....see if this helps:

2b^2 -50 = 0

2b^2 = 50

b^2 = 25

b = +- 5

Dec 20, 2020
#2
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
+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

CPhill Dec 20, 2020