已知x+√(x^2-1) +1/[x-√(x^2-1)]=20,则x^2+√(x^4-1)+1/[x^2+√(x^4-1)的值
问题描述：
已知x+√(x^2-1) +1/[x-√(x^2-1)]=20,则x^2+√(x^4-1)+1/[x^2+√(x^4-1)的值
答
x+√(x^2-1) +1/[x-√(x^2-1)]=20
x+√(x^2-1) +x-√(x^2-1) =20
2x=20
x=10
x^2+√(x^4-1)+1/[x^2+√(x^4-1)
=x^2+√(x^4-1)+([x^2-√(x^4-1)]/[x^2+√(x^4-1)][x^2-√(x^4-1)]
=x^2+√(x^4-1)+x^2-√(x^4-1)
=2x^2
=2*100
=200
答
1/[x-√(x^2-1)]=x+√(x^2-1) (分母有理化）,所以已知式子化简为x+√(x^2-1)=10,同理所求式化简为2x^2,利用已知式子解出x=101/20,代入所求式即可