Question

i will make brainlist answer

Answer 1

Answer:

2 or -1

Step-by-step explanation:

Let $i = \sqrt{2+\sqrt{2+\sqrt{2+....\alpha }}}$

Now, in $i$,

The sum after the first square root is the same as the value in variable $i$.

∴$i = \sqrt{2+i}$

Squaring both sides,

∴$i^{2} = 2 + i$

∴$i^{2} - i - 2 = 0$

Solve it as a quadratic equation,

∴$i^{2} - 2i + i - 2 = 0$

∴$i(i-2)+1(i- 2) = 0$

∴$(i + 1) (i - 2) = 0$

∴ $i + 1 = 0$         OR        $i - 2 = 0$

∴$i = -1$               OR        $i = 2$