solve-x-2-1-2-x-

Question Number 26320 by byaw last updated on 24/Dec/17

solve x^{2} - 1 = 2^{x}

Commented by mrW1 last updated on 24/Dec/17

o n e s o l u t i o n i s x = 3 .

Commented by jota@ last updated on 24/Dec/17

b y g r a p h i n g o t h e r s o l u t i o n i s

x \approx - 1.2

Commented by mrW1 last updated on 25/Dec/17

t h e r e a r e t o t a l l y t h r e e s o l u t i o n s :

\approx - 1.19825

= 3

\approx 3.40745

Answered by ibraheem160 last updated on 24/Dec/17

\frac{1 \pm \sqrt{17}}{2}

Commented by mrW1 last updated on 24/Dec/17

t h e y {d o n}^{'} t s a t i s f y t h e e q u a t i o n .

Answered by ibraheem160 last updated on 24/Dec/17

{(1 + 1)}^{x} = x^{2} - 1

1 + x + \frac{x (x - 1) . 1^{2} + \dots . \infty}{2!} = x^{2} - 1

2 + 2 x + x^{2} - x = 2 x^{2} - 2

x^{2} - x - 4 = 0

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

x = \frac{1 \pm \sqrt{17}}{2}

Commented by Rasheed.Sindhi last updated on 26/Dec/17

The bionomial expansion

{(1 + y)}^{x} = 1 + \frac{x}{1} y + \frac{x (x - 1)}{1.2} y^{2}

+ \frac{x (x - 1) (x - 2)}{1.2.3} y^{3} + \dots

+ \frac{x (x - 1) \dots (x - r + 1)}{1.2 \dots . r} x^{r} + \dots

holds only when ∣ y ∣< 1 .

You have used it for y = 1