Question

if x= 1 / 2-√3 then find the value of x^2-4x+1​

Answer 1

$\rm\blue{GIVEN}$

• if x=$\dfrac{1}{2-\sqrt{3}}$

$\rm\blue{TO\:FIND}$

• $\rm\red{x^{2}-4x+1}$

$\rm\blue{HOW\:TO\:SOLVE}$

• We will Rationalise the value of x

• We will take x as a Common and put the value of x.

$\implies\rm\red{x=\dfrac{1}{2-\sqrt{3}}}$

$\implies\rm\red{x=\dfrac{1}{2-\sqrt{3}}×\dfrac{2+\sqrt{3}}{2+\sqrt{3}}}$

$\implies\rm\red{x=\dfrac{2+\sqrt{3}}{1}}$

$\implies\rm\red{x=\dfrac{2+\sqrt{3}}{1}}$

• Squaring the both sides.

$\implies\rm\red{(x)^2=(\dfrac{2+\sqrt{3}}{1}})^2}$

$\implies\rm\red{x^2=4+4\sqrt{3}+3}$

$\implies\rm\red{x^2=7+4\sqrt{3}}$

Again,

$\implies\bf\blue{x^2-4x+1}$

• Put the value of x and x² in the given equation

$\implies\bf\blue{7+4\sqrt{3}-(4(2+\sqrt{3})+1}$

$\implies\bf\blue{7+{\cancel{4+\sqrt{3}}}-8-{\cancel{4+\sqrt{3}}}+1}$

$\implies\bf\blue{8-8=0}$

Hence,The value of $\rm\red{x^{2}-4x+1}$ is 0