Question

If x = 2+√3, prove that x2 - 4x + 1 = 0

Answer 1

Answer:

I know three methods...

Step-by-step explanation:

Method 1)

Checking if $x=2+\sqrt{3}$ is true for $x^2-4x+1=0$.

$(2+\sqrt{3} )^2-4(2+\sqrt{3} )+1\\=7+4\sqrt{3} -8-4\sqrt{3} +1\\=0$

∴$x=2+\sqrt{3}$(True)

Method 2)

Using Quadratic Formula

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

∴$x=2\frac{+}{} \sqrt{3}$(True)

Method 3)

Making Quadratic Equation from Root

($i$) Move $x$ and rationals to the left hand side.

($ii$) Leave square roots on the right hand side.

(The root and conjugate root is its roots.)

$x-2=\sqrt{3}$

$x^2-4x+4=3$

∴$x^2-4x+1=0$(True)

Answer 2

Step-by-step explanation:

2-root 3

suppose, One Zero is alpha and other Is Beta , Then Alpha + Beta = -Coefficient of x/coefficient of X2

putting aplha Value in it

Beta = 4-2-root3

Beta = 2-root3