Question

If x = 2-√3, then find the value of x square

Answer 1

Given :

$\sf x \:=\: 2\:-\: \sqrt3$ --- equation 1

To find :

Value of $\sf{x}^{2}$

Solution :

To find value of $\sf{x}^{2}$ .We have to square equation 1

→$\sf {x}^{2} \:=\:{( 2\:-\: \sqrt3)}^{2}$

Using identity → $\sf {( a - b )}^{2}$ = $\sf {a}^{2} + {b}^{2} - 2ab$

→$\sf {x}^{2} \:=\: {2}^{2}\:+\:{\sqrt3}^{2} \:-\: 2(2)(\sqrt3)$

→$\sf {x}^{2} \:=\:4\:+\:3\:-\:4\sqrt3$

→$\sf {x}^{2} \:=\: 7\:-\: 4\sqrt3$

FINAL ANSWER = $\sf {x}^{2} \:=\: 7\:-\: 4\sqrt3$