Question

If x=root3-root2/root3+root2 and y=root3+root2/root3-root2 find the vale of x square + y square+xy​

Answer 1

x = (√3 + √2) / (√3 - √2)

y = (√3 - √2) / (√3 + √2)

x^2 + y^2

= [(√3 + √2) / (√3 - √2)]^2 + [(√3 - √2) / (√3 + √2)]^2

= [(√3 + √2)^2 / (√3 - √2)^2] + [(√3 - √2)^2 / (√3 + √2)^2]

= [(3 + 2√6 + 4) / (3 - 2√6 + 4)] + [(3 - 2√6 + 4) / (3 + 2√6 + 4)]

= [(7 + 2√6) / (7 - 2√6)] + [(7 - 2√6) / (7 + 2√6)]

= [(7 + 2√6)^2 / (49 - 24)] + [(7 - 2√6)^2 / (49 - 24)] -- rationalizing the denominators

= [(49 + 28√6 + 24) / 50] + [(49 - 28√6 + 24) / 50]

= [(73 + 28√6) / 50] + [(73 - 28√6) / 50]

= (73 + 28√6 + 73 - 28√6) / 50

= 146/50

= 73/25

Answer 2

Answer:

please see the attachment