已知(x²+y²)(x²+y²+5)-6=0求代数式x²+y²的值
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已知(x²+y²)(x²+y²+5)-6=0求代数式x²+y²的值
已知(x²+y²)(x²+y²+5)-6=0求代数式x²+y²的值
已知(x²+y²)(x²+y²+5)-6=0求代数式x²+y²的值
(x²+y²)(x²+y²+5)-6=0
(x^2+y^2)^2+5(x^2+y^2)-6=0
(x^2+y^2+6)(x^2+y^2-1)=0
∴x^2+y^2=1
令m=x^2+y^2,则m>=0
原式=m(m+5)-6=m^2+5m-6=(m+6)(m-1)=0
解得m=-6(舍去),m=1
所以,x^2+y^2=1