Question

[Tran Le Hoang Yen]

Bài 1 : Chứng minh rằng với mọi số nguyên n

a) \(\left(n^2+3n-1\right)\left(n+2\right)-n^3+2\) chia hết cho 5

b)\(n\left(n+5\right)-\left(n-3\right)\left(n+2\right)\)chia hết cho 6

c)\(\left(n-1\right)\left(n+1\right)-\left(n-7\right)\left(n-5\right)\)chia hết cho 12

Bài 2:

Tìm x biết : \(\left(4x+3_{^{ }}\right)^3+\left(5-7x\right)^3+\left(3x-8\right)^3=0\)

Answer 1

[An Nguyễn Bá]

Bài 2:Tìm x biết

\\(\\left(4x+3\\right)^3+\\left(5-7x\\right)^3+\\left(3x-8\\right)^3=0\\)

\\(\\Leftrightarrow\\left[\\left(4x\\right)^3+3.\\left(4x\\right)^2.3+3.4x.3^2+3^3\\right]+\\left[5^3-3.5^2.7x+3.5.\\left(7x\\right)^2-\\left(7x\\right)^3\\right]+\\left[\\left(3x\\right)^3-3.\\left(3x\\right)^2.8+3.3x.8^2-8^3\\right]=0\\)

\\(\\Leftrightarrow64x^3+144x^2+108x+27+125-525x+735x^2-343x^3+27x^3-216x^2+576x-512=0\\)

\\(\\Leftrightarrow-252x^3+663x^2+159x-360=0\\)

\\(\\Leftrightarrow3\\left(-84x^3+221x^2+53x-120\\right)=0\\)

Answer 2

[Nguyen Nguyen]

M bị phê đá à con