Question

if x= root3+1/root3-1 and y= root 3 -1/root 3 +1 then find x 2 +y 2 +xy

Answer 1

Step-by-step explanation:

$given \: x = \frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 } \: and \: y = \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } \\ then \: x {}^{2} + y {}^{2} + xy = ( \frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 }) {}^{2} +(\frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 }) {}^{2} +( \frac{ \sqrt{3} + 1}{ \sqrt{3} - 1 })(\frac{ \sqrt{3} -1}{ \sqrt{3} + 1 }) \\ = \frac{4}{2} + \frac{2}{4} + ( \frac{3 - \sqrt{3} + \sqrt{3} - 1}{3 - 1}) \\ = 2 + \frac{1}{2} + \frac{2}{2} = 2 + \frac{1}{2} \\ = \frac{5}{2} = 2.5$