Question

Известно, что +−+−+=3
x
+
y
x
−
y
+
x
−
y
x
+
y
=
3
. Найдите значение выражения 2+22−2+2−22+2
x
2
+
y
2
x
2
−
y
2
+
x
2
−
y
2
x
2
+
y
2
.СРОЧНО

Answer 1

$\displaystyle\bf} \frac{x+y}{x-y} +\frac{x-y}{x+y} =3 ; \quad ODZ: x\neq y ;\quad x\neq -y\\\\\\\frac{(x+y)^2+(x-y)^2}{(x+y)(x-y)} =3\\\\\\\frac{x^2+x^2+2xy-2xy+y^2+y^2}{x^2-y^2} =3\\\\\\\frac{2x^2+2y^2}{x^2-y^2} =3\\\\2x^2+2y^2=3x^2-3y^2\\\\\boxed{x^2=5y^2}\\\\\frac{x^2+y^2}{x^2-y^2} +\frac{x^2-y^2}{x^2+y^2} =\frac{5y^2+y^2}{5y^2-y^2} +\frac{5y^2-y^2}{5y^2+y^2} =\frac{6}{4} +\frac{4}{6} =\frac{18+8}{12} =\boxed{\frac{13}{6} } \\\\Otvet: \boxed{\frac{13}{6}}$