Toán Lớp 8: Phân tích đa thức thành nhân tử : x³ +2x+x²
Tìm x: a,x²(x²+1)-x²-1
b,5x(x-3)²-5(x-1)³+15(x+2)(x-2)
Leave a reply
Register Now
Login
Lost Password
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Toán Lớp 8: Phân tích đa thức thành nhân tử : x³ +2x+x²
Tìm x: a,x²(x²+1)-x²-1
b,5x(x-3)²-5(x-1)³+15(x+2)(x-2)
Comments ( 1 )
{x^3} + 2x + {x^2}\\
= x.\left( {{x^2} + 2 + x} \right)\\
= x.\left( {{x^2} + x + 2} \right)\\
a){x^2}\left( {{x^2} + 1} \right) – {x^2} – 1\\
= {x^2}\left( {{x^2} + 1} \right) – \left( {{x^2} + 1} \right)\\
= \left( {{x^2} + 1} \right)\left( {{x^2} – 1} \right)\\
= \left( {{x^2} + 1} \right)\left( {x + 1} \right)\left( {x – 1} \right)\\
Khi:{x^2}\left( {{x^2} + 1} \right) – {x^2} – 1 = 0\\
\Leftrightarrow \left( {{x^2} + 1} \right)\left( {x + 1} \right)\left( {x – 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 1\\
x = – 1
\end{array} \right.\\
Vay\,x = 1;x = – 1\\
b)5x{\left( {x – 3} \right)^2} – 5{\left( {x – 1} \right)^3} + 15\left( {x + 2} \right)\left( {x – 2} \right)\\
= 5x\left( {{x^2} – 6x + 9} \right) – 5\left( {{x^3} – 3{x^2} + 3x – 1} \right)\\
+ 15\left( {{x^2} – 4} \right)\\
= 5{x^3} – 30{x^2} + 45x – 5{x^3} + 15{x^2} – 15x + 5\\
+ 15{x^2} – 60\\
= 30x – 55\\
Khi:30x – 55 = 5\\
\Leftrightarrow 30x = 60\\
\Leftrightarrow x = 2\\
Vay\,x = 2
\end{array}$