x=2 y=3

\(49x^2+14x-16y^2+2023^0=49x^2+14x+1-16y^2\)

\(=\left(7x+1\right)^2-\left(4y\right)^2=\left(7x+1-4y\right)\left(7x+1+4y\right)\)

\(A=\left(x+7\right)^2-\left(4y\right)^2=\left(x-4y+7\right)\left(x+4y+7\right)\)

\(B=y\left(x-y\right)-\left(x-y\right)=\left(y-1\right)\left(x-y\right)\)

\(C=x^4-x^2-4x^2+4=x^2\left(x^2-1\right)-4\left(x^2-1\right)\)

\(=\left(x^2-4\right)\left(x^2-1\right)=\left(x-2\right)\left(x-1\right)\left(x+1\right)\left(x+2\right)\)

x=13 nên x+1=14

\(M=x^5-x^4\left(x+1\right)+x^3\left(x+1\right)-x^2\left(x+1\right)+x\left(x+1\right)-1\)

\(=x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-1\)

=x-1

=13-1=12

TL

T i k cho mik ik rồi mik Trả lời cho

#Kirito

Kb nha ,mik sẽ trả lời giúp bạn 

Bài này là bài ktra hk 2 của mình 

\(\dfrac{7x^3+14x^2+7x}{14x^2+14x}=\dfrac{7x\left(x^2+2x+1\right)}{14x\left(x+1\right)}=\dfrac{\left(x+1\right)^2}{2\left(x+1\right)}=\dfrac{x+1}{2}\)

\(\dfrac{7x^3+14x^2+7x}{14x^2+14x}=\dfrac{7x\left(x^2+2x+1\right)}{14x\left(x+1\right)}=\dfrac{7x\left(x+1\right)^2}{14x\left(x+1\right)}=\dfrac{\left(x+1\right)}{2}\)

Bài 1:

\(f\left(x\right)=x^2+8x+25\)

Cho \(f\left(x\right)=0\Rightarrow x^2+8x+25=0\)

\(\Rightarrow x^2+8x+16+9=0\)

\(\Rightarrow\left(x+4\right)^2+9=0\)

Dễ thấy: \(\left(x+4\right)^2\ge0\forall x\)

\(\Rightarrow\left(x+4\right)^2+9\ge9>0\forall x\) ( vô nghiệm )

Vậy đa thức \(f\left(x\right)=x^2+8x+25\) không có nghiệm

Bài 2:

\(f\left(x\right)=x^{14}-14x^{13}+14x^{12}-...+14x^2-14x+14\)

\(f\left(x\right)=x^{14}-\left(13+1\right)x^{13}+\left(13+1\right)x^{12}-...+\left(13+1\right)x^2-\left(13+1\right)x+\left(13+1\right)\)

Do \(f\left(x\right)=13\) nên ta chỗ nào có \(13\) ta thay bằng \(x\)

\(f\left(13\right)=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-...+\left(x+1\right)x^2-\left(x+1\right)x+\left(x+1\right)\)

\(f\left(13\right)=x^{14}-x^{14}-x^3+x^{13}+x^{12}-...+x^3+x^2-x^2-x+x+1=1\)

Vậy \(f\left(13\right)=1\)