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b: \(=\left(x^2+3x+1-3x+1\right)^2=\left(x^2+2\right)^2\)
\(A=\left(2^2+4^2+...+100^2\right)-\left(1^2+3^2+...+99^2\right)\)
\(A=2^2-1^2+4^2-3^2+...+100^2-99^2\)
\(A=\left(2-1\right)\left(2+1\right)+\left(4-3\right)\left(4+3\right)+...+\left(100-99\right)\left(100+99\right)\)
\(A=1\left(1+2\right)+1\left(3+4\right)+....+1\left(99+100\right)\)
\(A=1+2+3+4+....+99+100\)
A=5050
\(B=3^8.7^8-\left(21^4-1\right)\left(21^4+1\right)\)
\(B=\left(3.7\right)^8-\left(21^8-1\right)\)
\(B=21^8-21^8+1\)
B=1
mà A=5050
⇒ A>B
Làm dễ hiểu chút
\(A=\left(2^2+4^2+...+100^2\right)-\left(1^2+3^2+...+99^2\right)\)
\(=\left(2^2-1^2\right)+\left(4^2-3^2\right)+...+\left(100^2-99^2\right)\)
\(=\left(2+1\right)\left(2-1\right)+\left(4+3\right)\left(4-3\right)+...+\left(100-99\right)\left(99+100\right)\)
\(=3+7+...+199\)
\(B=3^8.7^8-\left(21^4-1\right)\left(21^4+1\right)\)
\(=21^8-\left(21^8-1\right)=1\)
Vậy A > B
Nếu đúng đề thì là bằng 9 hoặc 16
Còn nếu bạn ghi thiếu số 8 + 11 thì bằng 96
k cho mk nha
\(a,2\left(x-1\right)-3x\left(x-5\right)=21\)
\(\Leftrightarrow2x-2-3x^2+15x-21=0\)
\(\Leftrightarrow-3x^2+17x-23=0\)
\(\Leftrightarrow-3\left(x^2+17x+\dfrac{298}{4}\right)+\dfrac{401}{2}=0\)
\(\Leftrightarrow-3\left(x+\dfrac{17}{2}\right)^2=-\dfrac{401}{2}\)
\(\Leftrightarrow\left(x+\dfrac{17}{2}\right)^2=\dfrac{401}{6}\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{17}{2}=\sqrt{\dfrac{401}{6}}\\x+\dfrac{17}{2}=-\sqrt{\dfrac{401}{6}}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{401}{6}}-\dfrac{17}{2}\\x=-\sqrt{\dfrac{401}{6}}-\dfrac{17}{2}\end{matrix}\right.\)
\(b,\left(x+3\right)-\left(x-4\right)\left(x+8\right)=1\)
\(\Leftrightarrow x+3-x^2-4x+32-1=0\)
\(\Leftrightarrow x^2-3x+34=0\)
\(\Leftrightarrow\left(x^2-3x+\dfrac{9}{4}\right)+\dfrac{127}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{3}{2}\right)^2=-\dfrac{127}{4}\)
Ta có:
\(\left(x-\dfrac{3}{2}\right)^2\ge0\forall x\)
Vậy pt vô nghiệm