if X equals to 1 upon root 3 minus root 2 and y equals to 1 upon root 3 + root 2 find x square - 5 xy + Y square
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X = 1/√3 - √2. y = 1/√3 + √2
X = 1-√6 /√3. y = 1+√6 / √3
= x^2 - 5xy + y^2
= {(1-√6 /√3)^2} - 5 (1-√6 /√3.)(1+√6 / √3) + {(1+√6 / √3)^2}
= {(1-2√6+6 / 3)} -5(1-2) +{ (1+2√6+6 / 3)}
= (7-2√6 / 3) +5 + (7+2√6 / 3)
= (7-2√6 / 3) +15/3 + (7+2√6 / 3)
= (7-2√6) + 15 + (7+2√6)
= 7-2√6+15+7+2√6
= 29
X = 1-√6 /√3. y = 1+√6 / √3
= x^2 - 5xy + y^2
= {(1-√6 /√3)^2} - 5 (1-√6 /√3.)(1+√6 / √3) + {(1+√6 / √3)^2}
= {(1-2√6+6 / 3)} -5(1-2) +{ (1+2√6+6 / 3)}
= (7-2√6 / 3) +5 + (7+2√6 / 3)
= (7-2√6 / 3) +15/3 + (7+2√6 / 3)
= (7-2√6) + 15 + (7+2√6)
= 7-2√6+15+7+2√6
= 29
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