Question

[Vũ Anh Tú]

Cho \(x+\frac{1}{x}=a\) Tính giá trị biểu thức theo a

A = \(x^2+\frac{1}{x^2}\)

B \(x^3+\frac{1}{x^3}\)

C = \(x^5+\frac{1}{x^5}\)

Answer 1

[Moon Light]

a)Ta có:a²=(x+1/x)²=x²+2+1/x²

=>A=x²+1/x²=a²-2

b)Ta có:a(a²-2)=(x+1/x)(x²+1/x²)=x³+1/x³+x+1/x

=>B=x³+1/x³=a(a²-2)-x-1/x=a(a²-2)-a=a(a²-3)

c)Ta có:(a²-2).a(a²-3)-a=(x²+1/x²)(x³+1/x³)-x-1/x=x⁵+1/x⁵+x+1/x-x-1/x=x⁵+1/x⁵=C

Answer 2

[quan]

a)x^2+1/x^2=x^2+2+1/x^2-2=(x+1/x)^2-2=a^2-2

b) (x+1/x)^3-3x-3/x=a^3-3(x+1/x)=a^3-3a

c) minh dang nghi