Question 83

If $$2+x\sqrt{3}$$=$$\frac{1}{2+\sqrt{3}}$$ then the simplest value of x is

Solution

$$2+x\sqrt{3}$$ = $$\frac{1}{2+\sqrt{3}}$$

Rationalizing the R.H.S.

=> $$2+x\sqrt{3}$$ = $$\frac{1}{2+\sqrt{3}}$$ * $$\frac{2-\sqrt{3}}{2-\sqrt{3}}$$

=> $$2+x\sqrt{3}$$ = $$\frac{2-\sqrt{3}}{4-3}$$

=> $$2+x\sqrt{3}$$ = $$2-\sqrt{3}$$

Comparing both sides, we get $$x$$ = -1

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