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
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
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
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