已知实数xy满足4/x^4-2/x^2=3,y^4+y^2=3则 4/x^4+y^4的值为?只要简略步骤
问题描述:
已知实数xy满足4/x^4-2/x^2=3,y^4+y^2=3则 4/x^4+y^4的值为?只要简略步骤
答
4/x^4-2/x^2=3,(2/x^2-1/2)^2=13/4,2/x^2=(√ 13+1)/2
y^4+y^2=3,(y^2+1/2)^2=13/4,y^2=(√ 13-1)/2
4/x^4+y^4=(2/x^2)^2+(y^2)^2=7