Question

If x = 2 root 3 + root 2 and y = 2 root 3 minus root 2 then what is the relation between X and y

Answer 1

Answer:

$x = 2 \sqrt{3} + \sqrt{2} - (i)\\ y = 2 \sqrt{3} - \sqrt{2} - (ii)\\\blue{\mathfrak{\underline{\large{Divide \: (i)\:by \: (ii)}}}:} \\ \frac{x}{y} = \frac{2 \sqrt{3} + \sqrt{2} }{2 \sqrt{3} - \sqrt{2} } \\ \frac{x}{y} = \frac{2 \sqrt{3} + \sqrt{2} }{2 \sqrt{3} - \sqrt{2} } \times \frac{2 \sqrt{3} + \sqrt{2} }{2 \sqrt{3} + \sqrt{2} } \\ \frac{x}{y} = \frac{ {(2 \sqrt{3} + \sqrt{2} )}^{2} }{ {(2 \sqrt{3} )}^{2} - {( \sqrt{2} )}^{2} } \\ \frac{x}{y} = \frac{12 + 2 + 4 \sqrt{6} }{12 - 2} \\ \frac{x}{y} = \frac{14 + 4 \sqrt{6} }{10} \\ \frac{x}{y} = \frac{2(7 + 2 \sqrt{6} )}{10} \\ \frac{x}{y} = \frac{7 + 2 \sqrt{6} }{5} \\ \blue{\mathfrak{\underline{\large{Cross \: multiply}}}:} \\ 5x = (7 + 2 \sqrt{6} )y \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \green{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$