Question

If (m2 - 4m - 1) = 0, then determine the value of (m + m-1). (given: m < 1)

Answer 1

2m-4m-1=0 then m= 1/2

Answer 2

Answer:

-5 - √5

Step-by-step explanation:

Given equation,

$m^2-4m-1=0$

By the quadratic formula,

$m=\frac{-(-4)\pm \sqrt{(-4)^2-4\times 1\times -1}}{2}$

$m=\frac{-4\pm \sqrt{16+4}}{2}$

$m=\frac{-4\pm \sqrt{20}}{2}$

$m=\frac{-4\pm 2\sqrt{5}}{2}$

$m=-2\pm \sqrt{5}$

∵ √5 > -2 ⇒ -2 + √5 = Positive and -2 - √5 = negative,

Here, m < 1

$\implies m = -2-\sqrt{5}$

$\implies m + m-1 = -2 - \sqrt{5} - 2 -\sqrt{5} - 1 = -5 - \sqrt{5}$