Question

x² - y² + 1 - ( x² * y² )

Answer 1

Answer:

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Step-by-step explanation:

We can start this by completing the square.So,bringing 4 from the LHS to the RHS,the LHS can be written as x^2+1/x^2+y^2+1/y^2–4=0.Now,we write -4 as -2–2,and distribute each of the -2 to each of the variables(namely x and y).So,we get (x^2+1/x^2–2)+(y^2+1/y^2–2)=0.Now,on completing the squares for the two terms in the brackets in the LHS,we get (x-1/x)^2+(y-1/y)^2=0.Now,remember the sum of squares of two quantities is 0 only when each and every one of them is 0.So,we get x-1/x=0=>x^2=1.

y-1/y=0=>y^2=1 which implies x^2+y^2=2

Answer 2

x² - y² + 1 - (x²y²)

= (x² - x²y²) + (1 - y²)

= x²(1 - y²) + 1(1 - y²)

= (x² + 1)(1 - y²)