Question

se xy=27 e (x-y)=10, qual é o valor da expressão (x²-y²)?

Answer 1

$xy=27\\x=\frac{27}{y}\\x^2-y^2=10\\(\frac{27}{y})^2-y^2=\frac{729}{y^2}-y^2=\frac{720y^2-y^4}{y^2}=10\\\\720y^2-y^4=10y^2\\720y^2-y^4-10y^2=0\\-y^4+700y^2=0\\y^4-700y^2=0\\y^4=x^2\\y^2=x\\x^2-700x=0\\x(x-700)=0\\x'=0\\x''-700=0\\x''=700\\y^2=0\\\boxed{y'=0}\\y^2=700\\\boxed{y''=\pm\sqrt{700}}$