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a) \(\left(2x+1\right)^2+2.\left(2x+1\right)+1=\left(2x+2\right)^2\)
b) \(\left(3x-2y\right)^2+4.\left(3x-2y\right)+4\)
\(=\left(3x-2y\right)^2+2.\left(3x-2y\right).2+2^2\)
\(=\left(3x-2y+2\right)^2\)
\(1,\left(2x+1\right)^2+2\left(2x+1\right)+1\\ =\left(2x+1\right)^2+2.\left(2x+1\right).1+1^2\\ =\left[\left(2x+1\right)+1\right]^2\\ b,\left(3x-2y\right)^2+4\left(3x-2y\right)+4\\ =\left(3x-2y\right)^2+2.\left(3x-2y\right).2+2^2\\ =\left[\left(3x-2y\right)+2\right]^2\)
1) \(\left(2x+1\right)^2+2\left(2x+1\right)+1\)
\(=\left(2x+1\right)^2+2\left(2x+1\right)\cdot1+1^2\)
\(=\left[\left(2x+1\right)+1\right]^2\)
\(=\left(2x+2\right)^2\)
2) \(\left(3x+2y\right)^2+4\left(3x+2y\right)+4\)
\(=\left(3x+2y\right)^2+2\cdot\left(3x+2y\right)\cdot2+2^2\)
\(=\left[\left(3x+2y\right)+2\right]^2\)
\(=\left(3x+2y+2\right)^2\)
\(\left(x+2y\right)^2-\left(x-2y\right)^2\\ =\left[\left(x+2y\right)-\left(x-2y\right)\right]\left[\left(x+2y\right)+\left(x-2y\right)\right]\\ =\left(x+2y-x+2y\right)\left(x+2y+x-2y\right)\\ =4y.\left(2x\right)\\ =8xy\)
\(\left(3x+y\right)^2+\left(x-y\right)^2\\ =\left[\left(3x\right)^2+2.3x.y+y^2\right]+\left(x^2-2xy+y^2\right)\\ =6x^2+6xy+y^2+x^2-2xy-y^2\\ =7x^2+4xy\)
\(-\left(x+5\right)^2-\left(x-3\right)^2\\ =-\left(x^2+10x+25\right)-\left(x^2-6x+9\right)\\ =-x^2-10x-25-x^2+6x-9\\ =-2x^2-4x-34\)
\(\left(3x-2\right)^2-\left(3x-1\right)^2\\ =\left[\left(3x-2\right)-\left(3x-1\right)\right]\left[\left(3x-2\right)+\left(3x-1\right)\right]\\ =\left(3x-2-3x+1\right)\left(3x-2+3x-1\right)\\ =-1.\left(6x-3\right)\\ =-6x+3\)
Ta có: \(A^2=\dfrac{\left(3x-2y\right)^2}{\left(3x+2y\right)^2}\)
\(=\dfrac{9x^2+4x^2-12xy}{9x^2+4x^2+12xy}\)
\(=\dfrac{20xy-12xy}{20x^2+12xy}\)
\(=\dfrac{8xy}{32xy}=\dfrac{1}{4}\)
\(\Leftrightarrow A\in\left\{\dfrac{1}{2};-\dfrac{1}{2}\right\}\)(1)
Vì 2y<3x<0 nên 3x-2y>0 và 3x+2y<0
hay \(A=\dfrac{3x-2y}{3x+2y}< 0\)(2)
Từ (1) và (2) suy ra \(A=-\dfrac{1}{2}\)
Vậy: \(A=-\dfrac{1}{2}\)
Sửa đề: \(5x^2y^2\cdot\left(3x^2\right)^3\)
\(=5x^2y^2\cdot27x^6\)
\(=5\cdot27\cdot x^2\cdot x^6\cdot y^2\)
\(=135x^8y^2\)
ta có
9x2+12xy+4y2=32xy
=>(3x+2y)2=32xy =>3x+2y=\(\sqrt{32xy}\)
mặt khác
9x2-12xy+4y2=8xy
=>(3x-2y)2=8xy =>3x-2y=\(\sqrt{8xy}\)
vậy \(\frac{3x-2y}{3x+2y}=\frac{\sqrt{8xy}}{\sqrt{32xy}}\)
=0,5
đề này có trong violimpic vòng 15
hôm qua mình đi thi có gặp bài này ko bt sai hay đúng nữa
mà hình như mình làm sai dấu
=\(\left(3x^2-2y^2\right)\left(3x^2-3x^2+2y^2\right)\)
=\(\left(3x^2-2y^2\right)\cdot2y^2\)