If 2a + b = 10, 2ab = 9, and 2a > b, then find the value of 2a – b.

We know that,

If x + y  = n

then, x - y  = \(\sqrt {n^2 - 4xy}\)

If 2a + b = 10,

2ab = 9, and 2a > b,

then find the value of 2a – b

So, if 2ab = 9,

then, ab = 4.5

and the value of 2a – b = \(\sqrt {10^2 - 4(2)(4.5)}\)

= \(\sqrt {10^2 - 4(2)(4.5)}\) = \(\sqrt {64}\) = 8