Question

(x^2-3x+9)(3-x)=27-x^3

(x^3+x^2y+xy^2+y^3)(x-y)=x^4-y^4

Answer 1

a) 

\(3x^2-x^3-9x+3x^2+27-9x=27-x^3\) 

\(-x^3+6x^2-18x+27=27-x^3\) 

\(6x^2-18x=0\) 

\(6x\left(x-3\right)=0\) 

\(\orbr{\begin{cases}6x=0\\x-3=0\end{cases}}\) 

\(\orbr{\begin{cases}x=0\\x=3\end{cases}}\) 

b) 

\(x^4-x^3y+x^3y-x^2y^2+x^2y^2-xy^3+xy^3-y^4=x^4-y^4\) 

\(x^4-y^4=x^4-y^4\) 

\(0=0\left(llđ\forall x\right)\) 

Answer 2

a) ( x² - 3x + 9 )( 3 - x ) = 27 - x³

<=> -x³ + 6x² - 18x + 27 = 27 - x³

<=> -x³ + 6x² - 18x + x³ = 27 - 27

<=> 6x² - 18x = 0

<=> 6x( x - 3 ) = 0

<=> \(\orbr{\begin{cases}6x=0\\x-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=3\end{cases}}\)

b) Ta có VP = ( x² )² - ( y² )²

                    = ( x² - y² )( x² + y² )

                    = ( x - y )( x + y )( x² + y² )

                    = ( x - y )[ ( x + y )( x² + y² ) ]

                    = ( x - y )( x³ + xy² + x²y + y³ ) = VT

Vậy phương trình nghiệm đúng với mọi x, y ∈ R

Answer 3

a,\(\left(x^2-3x+9\right)\left(3-x\right)=27-x^3\)

\(27-x^3=27-x^3\)

b,\(\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)=x^4-y^4\)

\(VP=x^4-y^4\)

\(=\left(x^2\right)^2-\left(y^2\right)^2\)

\(=\left(x^2-y^2\right)\left(x^2+y^2\right)\)

\(=\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\)

\(=\left(x-y\right)\left(x^3+xy^2+x^2y+y^3\right)\)

\(\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)=VP\)