If $$x = \dfrac{2+\sqrt{3} }{2-\sqrt{3} } $$, then the value of $$(x-7)^2$$

Question

If $$x = \dfrac{2+\sqrt{3}  }{2-\sqrt{3}  }  $$, then the value of $$(x-7)^2$$

Uniteasy Admin · Accepted Answer

$$ x = \dfrac{2+\sqrt{3}  }{2-\sqrt{3}  }  $$
$$=\dfrac{2+\sqrt{3}  }{2-\sqrt{3}  } \cdot \dfrac{2+\sqrt{3}}{2+\sqrt{3}}   $$
$$=(2+\sqrt{3})^2$$
$$=7+4\sqrt{3}  $$
$$(x-7)^2$$
$$=(4\sqrt{3} )^2=48$$

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