Find the square root of the polynomial- x^2/y^2+y^2/x^2−2(xy+yx)+3

motsetjela

motsetjela

Answered question

2022-08-10

Find the square root of the polynomial-
x 2 y 2 + y 2 x 2 2 ( x y + y x ) + 3

Answer & Explanation

vladinognm

vladinognm

Beginner2022-08-11Added 13 answers

Let t = x y + y x
Then t 2 = x 2 y 2 + y 2 x 2 + 2
Your "polynomial" becomes finally an actual polynomial:
t 2 2 2 t + 3 = t 2 2 t + 1 = ( t 1 ) 2 = ( x y + y x 1 ) 2 .
So, the two square roots are
± ( x y + y x 1 ) .

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