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(3x-4-x-1)(3x-4+x+1)=0
(2x-5)(4x-3)=0
2x-5 = 0 hoặc 4x-3=0
2x=5 hoặc 4x=3
x=5/2 hoặc x=3/4
\(A=\left(2x\right)^2+2.2x.\frac{1}{4}+\frac{1}{16}+\frac{1}{16}=\left(2x+\frac{1}{4}\right)^2+\frac{1}{16}\ge\frac{1}{16}\)
=> GTNN(A)=\(\frac{1}{16}\)
\(B=9x^2+2.3x.1+1+14=\left(3x+1\right)^2+14\ge14\)
=> GTNN(B)=14
x4 + x3 + 2x2 + 1
= (x4 + 2x2 + 1) + x3
= (x2 + 1)2 + x3
còn bài nào ko??
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\(x^4+x^3+2x^2+1\)
\(=\left(x^4+2x^2+1\right)+x^3\)
\(=\left(x^2+1\right)^2+x^3\)
\(a,A=0,2\left(5x-1\right)-\dfrac{1}{2}\left(\dfrac{2}{3}x+4\right)+\dfrac{2}{3}\left(3-x\right)\)
\(=x-0,2-\dfrac{1}{3}x-2+2-\dfrac{2}{3}x\)
\(=\left(-0,2-2+2\right)+\left(x-\dfrac{1}{3}x-\dfrac{2}{3}x\right)\)
\(=-0,2\)
\(b,B=\left(x-2y\right)\left(x^2+2xy+4y^2\right)-\left(x^3-8y^3+10\right)\)
\(=x^3-8y^3-x^3+8y^3-10\)
\(=-10\)
\(c,C=4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)-4x\)
\(=4\left(x^2+2x+1\right)+\left(4x^2-4x+1\right)-8\left(x^2-1\right)-4x\)
\(=4x^2+8x+4+4x^2-4x+1-8x^2+8-4x\)
\(=13\)
a) \(A=0,2\left(5x-1\right)-\dfrac{1}{2}\left(\dfrac{2}{3}x+4\right)+\dfrac{2}{3}\left(3-x\right)\)
\(A=x-\dfrac{1}{5}-\dfrac{1}{3}x-2+2-\dfrac{2}{3}x\)
\(A=\left(x-\dfrac{1}{3}x-\dfrac{2}{3}x\right)-\left(\dfrac{1}{5}+2-2\right)\)
\(A=-\dfrac{1}{5}\)
Vậy: ...
b) \(B=\left(x-2y\right)\left(x^2+2xy+4y^2\right)-\left(x^3-8y^3+10\right)\)
\(B=\left[x^3-\left(2y\right)^3\right]-\left[x^3-\left(2y\right)^3\right]-10\)
\(B=-10\)
Vậy: ...
c) \(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x+1\right)\left(x-1\right)-4x\)
\(=4\left(x^2+2x+4\right)+\left(4x^2-4x+1\right)-8\left(x^2-1\right)-4x\)
\(=4x^2+8x+4+4x^2-4x+1-8x^2+8-4x\)
\(=\left(4x^2+4x^2-8x^2\right)+\left(8x-4x-4x\right)+\left(4+1+8\right)\)
\(=13\)
Vậy:...
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(x^2-6x+8)(x^2-8x+15)+1
=(x^2-4x-2x+8)(x^2-5x-3x+15)+1
=(x(x-4)-2(x-4))(x(x-5)-3(x-5))+1
=(x-4)(x-2)(x-5)(x-3)+1
=(x-2)(x-5)(x-3)(x-4)+1
=(x^2-7x+10)(x^2-7x+12)+1
Gọi a=x^2-7x+11, ta có
(a-1)(a+1)+1
= a2 - 1 + 1
= a2
= (x2 - 7x + 11)2
Mình biết làm 1 cách thui, mong bạn thông cảm nha!
\(x^2-6x+8=0\Leftrightarrow x^2-2x-4x+8=0\)
\(\Leftrightarrow x\left(x-2\right)-4\left(x-2\right)=0\Leftrightarrow\left(x-2\right)\left(x-4\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x-2=0\\x-4=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=2\\x=4\end{cases}}}\)
Chúc may mắn nha!