Question

If u=e^x^2+2xy+y^2,then prove that Xu to the base x+yu to the base y= 2ulogu
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Answer 1

x2+y2=t−t1  and   x4+y4=t2+t21

⇒(x2+y2)2=(t−t1)2

⇒x4+y4+2x2y2=t2+t21−2

⇒x4+y4+2x2y2=x4+y4−2      [given]

⇒2x2y2=−2

⇒x2y2=−1

⇒y2=−x21

⇒y