Question

log2x^2=log2(根号2-1)-log2(根号2+1),求x+1/x

Answer 1

log2(x²)=log2[(√2-1)/(√2+1)]

log2(x²)=log2(√2-1)²

所以x²=(√2-1)²

x=±(√2-1)

x=√2-1

则1/x=√2+1

x+1/x=2√2

x=-√2+1

则1/x=-√2-1

x+1/x=-2√2

所以x+1/x=±2√2