已知x+1/x=4,求x的平方+1/x的平方,（x-1/x）的平方的值
网友回答
(x+1/x)^2
=x^2+2+1/x^2
=1616-2=14
x^2+1/x^2=14
(x-1/x)^2
=x^2+1/x^2-2
=(x^2+1/x^2+2)-4
=(x+1/x)^2-4
=4^2-4
=12======以下答案可供参考======
供参考答案1:
x²+1/x²
=x²+2+1/x²-2
=(x+1/x)²-2
=4²-2
=14(x-1/x)²
=x²-2+1/x²
=x²+1/x²-2
=14-2=12供参考答案2:
x+1/x=4
两边同时平方得
x²+2+1/x²=16
所以x²+1/x²=14
(x-1/x)²
=x²-2+1/x²
=(x²+1/x²)-2
=14-2=12供参考答案3:
x∧2 (1/x)∧2=14
(x-1/x)∧2=12