Question

Bài 2: Tìm đa thức P biết

a)x²+5x+6/x²+4x+4=P/x+2

b)a+1/a-1=(a+1)²/P

c)P/2a-6=a²+3a+9/2

d)a³+b³=(a-b).P

e)x²+y²=(x+y).P

Answer 1

Answer 2

a) Ta có: \(\dfrac{P}{x+2}=\dfrac{x^2+5x+6}{x^2+4x+4}\)

\(\Leftrightarrow\dfrac{P}{x+2}=\dfrac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)^2}=\dfrac{x+3}{x+2}\)

hay P=x+3

Answer 3

b) Ta có: \(\dfrac{\left(a+1\right)^2}{P}=\dfrac{a+1}{a-1}\)

\(\Leftrightarrow P=\left(a+1\right)\left(a-1\right)\)

\(\Leftrightarrow P=a^2-1\)

Answer 4

c) Ta có: \(\dfrac{P}{2a-6}=\dfrac{a^2+3a+9}{2}\)

\(\Leftrightarrow P=\left(a-3\right)\left(a^2+3a+9\right)\)

\(\Leftrightarrow P=a^3-27\)

Answer 5

d) Ta có: \(P\cdot\left(a-b\right)=a^3+b^3\)

nên \(P=\dfrac{a^3+b^3}{a-b}\)