已知实数a，b，x，y满足ax+by=3，ay-bx=5，试求(a²+b²)(x²+y²)的值

ax+by=3, 两边平方a^2x^2+2abxy+b^2y^2=9 (1) ay-bx=5，两边平方a^2y^2-2abxy+b^2x^2=25 (2) (2)+(1) a^2x^2+2abxy+b^2y^2+a^2y^2-2abxy+b^2x^2=34a^2(x^2+y^2)+b^2(x^2+y^2)=34(a^2+b^2)(x^2+y^2)=34