Question

Shows that, x^2-4x-1=0

Answer 1

Answer:

Answer:

The solutions to x2 + 4x + 1 = 0 are x = -2 + √(3) or x = -2 - √(3).

Step-by-step explanation:

^_^ Your Welcome!

Step-by-step explanation:

Answer 2

Answer:

$x =2± \sqrt{5}$

Step-by-step explanation:

${x}^{2} - 4x - 1 = 0$

1. Use the quadratic formula

$x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a}$

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

${x}^{2} −4−1=0 \\ a = 1 \\ b = - 4 \\ c = - 1 \\ x = \frac{ - ( - 4)± \sqrt{( - 4)^{2} } - 4⋅1( - 1)}{2.1}$

2. Simplify

1. Evaluate the exponent

$x = \frac{4±(−4)^{2} −4⋅1(−1)}{2.1} \\ x = \frac{4± \sqrt{16 - 4⋅1( - 1)} }{2⋅1}$

2. Multiply the numbers

$x = \frac{4± \sqrt{16 - 4⋅1( - 1)} }{2⋅1} \\ x = \frac{4± \sqrt{16 + 4} }{2⋅1}$

3. Add the numbers

$x = \frac{4± \sqrt{16 + 4} }{2⋅1} \\ x = \frac{4± \sqrt{20} }{2⋅1}$

4. Factorisation

$x = \frac{4± \sqrt{20} }{2⋅1} \\ x = \frac{4± \sqrt{2⋅10} }{2⋅1}$

5. Factorisation

$x = \frac{4± \sqrt{20} }{2⋅1} \\ x = \frac{4± \sqrt{2⋅2⋅5} }{2⋅1}$

6. Evaluate the square root

$x = \frac{4± \sqrt{2⋅2⋅5} }{2⋅1} \\ x = \frac{4± \sqrt{2}⋅ \sqrt{2} ⋅ \sqrt{5} }{2⋅1}$

7. Evaluate the square root

$x = \frac{4± \sqrt{2}⋅ \sqrt{2} ⋅ \sqrt{5} }{2⋅1} \\ x = \frac{4± \sqrt[2]{5}}{2⋅1}$

8. Multiply the numbers

$x = \frac{4± \sqrt[2]{5}}{2⋅1} \\ x = \frac{4± \sqrt[2]{5} }{2⋅1}$

3. Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

$x = \frac{4 + \sqrt[2]{5} }{2⋅1} \\ x = \frac{4 - \sqrt[2]{5}}{2⋅1}$

4. Solve

Rearrange and isolate the variable to find each solution

$x = 2 + \sqrt{5} \\ x = 2 - \sqrt{5}$

Solution

$x = 2± \sqrt{5}$