Question

Tìm các hệ số a,b,c bt rằng :

a, -3x^k ( ax² + bx + c ) = 3x^k+2 - 12x^k+1 + 3x^k ( với mọi x )

b, ( z² - z + 1 ) (az² + bz + c ) = 2z⁴ - z³ + 2z² + 1 với mọi x

Answer 1

a: \(\Leftrightarrow-3a\cdot x^{k+2}-3b\cdot x^{k+1}+3x^k=3x^{k+2}-12x^{k+1}+3x^k\)

=>-3a=3; -3b=-12

=>a=-1; b=4

b: \(\Leftrightarrow az^4+bz^3+cz^2-az^3-bz^2-cz+az^2+bz+c=2z^4-z^3+2z^2+1\)

\(\Leftrightarrow az^4+z^3\left(b-a\right)+z^2\left(c-b+a\right)+z\left(b-c\right)+c=2z^4-z^3+2z^2+1\)

=>c=1; b-c=0; c-b+a=2; b-a=-1; a=2

=>c=1; b=1; a=2