Question #0ff75

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Question #0ff75

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Answer 1 · 2017-05-13T14:43:22

$x^{2} + y^{2} + x y$ $x^2+y^2+xy$

$= x^{2} + y^{2} + 2 x y - x y$ $=x^2+y^2+2xy-xy$

$= {(x + y)}^{2} - x y$ $=(x+y)^2-xy$

$= {(\frac{\sqrt{2} + 1}{\sqrt{2} - 1} + \frac{\sqrt{2} - 1}{\sqrt{2} + 1})}^{2} - \frac{\sqrt{2} + 1}{\sqrt{2} - 1} \times \frac{\sqrt{2} - 1}{\sqrt{2} + 1}$ $=((sqrt2+1)/(sqrt2-1)+(sqrt2-1)/(sqrt2+1))^2-(sqrt2+1)/(sqrt2-1)xx(sqrt2-1)/(sqrt2+1)$

$= {⎛ ⎜ ⎜ ⎝ \frac{{(\sqrt{2} + 1)}^{2} + {(\sqrt{2} - 1)}^{2}}{2 - 1} ⎞ ⎟ ⎟ ⎠}^{2} - 1$ $=(((sqrt2+1)^2+(sqrt2-1)^2)/(2-1))^2-1$

$= {(\frac{2 (2 + 1)}{2 - 1})}^{2} - 1 = 6^{2} - 1 = 35$ $=((2(2+1))/(2-1))^2-1=6^2-1=35$

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Question #0ff75

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