`log_{2} ( x^2 + m + xsqrt{x^2 + 4} ) = (2m - 9)x - 1 + (1 - 2m)sqrt{x^2 + 4} (1)`

`<=> log_{2} (x^2 + m + x sqrt{x^2 + 4}) = 2m(x - sqrt{x^2 + 4}) - 9x - 1 + sqrt{x^2 + 4}`

 Đặt `t = log_{2} (x^2 + m + x sqrt{x^2 + 4})`

`to m = 2^t - x(x + sqrt{x^2 + 4})`

Khi đó phương trình `(1)` trở thành:

`to t = 2(2^t - x(x + sqrt{x^2 + 4}))(x - sqrt{x^2 + 4}) - 9x - 1 + sqrt{x^2 + 4}`

`to t = 2^(t + 1) . (x - sqrt{x^2 + 4}) - 2x(x + sqrt{x^2 + 4})(x - sqrt{x^2 + 4}) - 9x - 1 + sqrt{x^2 + 4}`

`to t = 2^(t + 1) . (x - sqrt{x^2 + 4}) - 2x(x^2 - x^2 - 4) - 9x - 1 + sqrt{x^2 + 4}`

`to t + 1 = 2^(t + 1) . (x - sqrt{x^2 + 4}) + sqrt{x^2 + 4} - x`

`to t + 1 = ( 2^(t + 1) - 1) . (x - sqrt{x^2 + 4}))`

`to t + 1 = 0 to t = -1`

`to m = 1/2 - x(x + sqrt{x^2 + 4}) = g(x)`

`g'(x) = -(x + sqrt{x^2 + 4}) - x . (1 + x/(sqrt{x^2 + 4}) ) < 0` với mọi `x`

`lim_{x to -oo} (1/2 - g(x)) = lim_{x to -oo} (x^2 + xsqrt{x^2 + 4}) = lim_{x to -oo} (x^4 - x^2(x^2 + 4))/(x^2 - xsqrt{x^2 + 4} ) = lim_{x to -oo} (-4x^2)/(x^2 - xsqrt{x^2 + 4}) = -2`

`to m < 1/2 + 2 = 5/2`

Vì `m \in [-20 ; 20] to m \in [-20 ; 5/2)`