Question

Tìm x

a, (3x -5). (7- 5x) - (5x+ 2). (2- 3x)= 4

 

b, (x+ 2). (x²- 2x+ 4)- (x³+ 3). x =14

Chứng minh rằng

a, \(\left(2n-3\right).n-2n.\left(n+2\right)⋮7\forall n\inℤ\)

b, \(n.\left(2n-3\right)-2n.\left(n+1\right)⋮5\forall n\inℤ\)

 

Answer 1

a) \(\left(3x-5\right)\left(7-5x\right)-\left(5x+2\right)\left(2-3x\right)=4\)

\(\Leftrightarrow-15x^2+46x-35+15x^2-4x-4=4\)

\(\Leftrightarrow42x-39=4\)

\(\Leftrightarrow42x=4+39\)

\(\Leftrightarrow42x=43\)

\(\Leftrightarrow x=\frac{43}{42}\)

\(\Rightarrow x=\frac{43}{42}\)

b) \(\left(x+2\right)\left(x^2-2x+4\right)-\left(x^3+3\right)x=14\)

\(\Leftrightarrow x^3+8-x^4-3x=14\)

\(\Leftrightarrow x^3+8-x^4-3x=14-14\)

\(\Leftrightarrow-x^4+x^3-3x-6=0\)

=> x k có gt thỏa mãn