Question

bài 1

cmr (a+b+c)^3-a^3 - b^3 - c^3=3*(a+b)*(b+c)*(c+a)

Bài 2

Cho x+1/x =3 tính giá trị biểu thức sau

a) x^2+1/x^2

b)x^3+1/x^3

Answer 1

1) \(\left(a+b+c\right)^3-a^3-b^3-c^3\)

\(=\left(a+b\right)^3+3\left(a+b\right)c\left(a+b+c\right)+c^3-a^3-b^3-c^3\)

\(=a^3+3ab\left(a+b\right)+b^3+3\left(a+b\right)c\left(a+b+c\right)-a^3-b^3\)

\(=3ab\left(a+b\right)+3\left(a+b\right)c\left(a+b+c\right)\)

\(=3\left(a+b\right)\left(ab+ac+bc+c^2\right)\)

\(=3\left(a+b\right)\left[a\left(b+c\right)+c\left(b+c\right)\right]\)

\(=3\left(a+b\right)\left(b+c\right)\left(a+c\right)\)

Answer 2

Bài 2:

a: \(x^2+\dfrac{1}{x^2}=\left(x+\dfrac{1}{x}\right)^2-2\cdot x\cdot\dfrac{1}{x}\cdot\left(x+\dfrac{1}{x}\right)=3^2-2\cdot3=3\)

b: \(x^3+\dfrac{1}{x^3}=\left(x+\dfrac{1}{x}\right)^3-3\cdot x\cdot\dfrac{1}{x}\left(x+\dfrac{1}{x}\right)\)

\(=3^3-3\cdot3=27-9=18\)