Solve questions early dear friendso

1.	Solve questions early dear friendso
Answer» Answer: $x=\sqrt[3]{<klux>2</klux>+\sqrt{3} }\\ x^{3}+\frac{1}{x^{3}} = ?$ ...........(1) We know that $x=\sqrt[3]{2+\sqrt{3} }$ TRANSPOSE ∛ to the other side, it becomes x³. $x^{3}={2+\sqrt{3} }$ ............ Substitute this in (1). The result is: ${2+\sqrt{3} }+\frac{1}{2+\sqrt{3} }$ Rationalise $\frac{1}{2+\sqrt{3} }$ . $2+\sqrt{3} +\frac{1}{2+\sqrt{3}}\frac{2-\sqrt{3} }{2-\sqrt{3} }$ $2+\sqrt{3} +\frac{2-\sqrt{3} }{(2+\sqrt{3)(2-\sqrt{3})}}$ ................(2)* We know that (a+B)(a-b)=a²-b² (2+√3)(2-√3)⇒2²-(√3)³⇒4-3⇒1. Thus, (2+√3)(2-√3)=1.......Substitute this in (2). $2+\sqrt{3} +\frac{2-\sqrt{3} }{1}$ $2+\sqrt{3} +{2-\sqrt{3}$ ......(REARRANGE the terms) $2+2+\sqrt{3}-\sqrt{3}$ ....................(-√3 and √3 gets cancelled, 2+2=4.) =4 Thus, (b) is the correct option. HOPE THIS HELPS :D

Answer»

Answer:

$x=\sqrt[3]{<klux>2</klux>+\sqrt{3} }\\ x^{3}+\frac{1}{x^{3}} = ?$ ...........(1)