tính :
(4 x 16)+(16x2)
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\(a,=\left(5x-1\right)^2\\ b,=\left(x+4\right)^2\\ c,=\left(4x+3y\right)^2\\ d,=\left(\dfrac{x}{4}+2y\right)^2\)
Đơn giản mà em cô sẽ chứng minh cho em thấy ngay bây giờ ha.
320 : ( 16 \(\times\) 2 ) = 320 : 16 : 2
Ta có:
320 : ( 16 \(\times\) 2)
= 320 : ( \(\dfrac{16\times2}{1}\) )
= 320 \(\times\) \(\dfrac{1}{16\times2}\)
= \(\dfrac{320}{16\times2}\)
= \(\dfrac{320}{16}\) \(\times\) \(\dfrac{1}{2}\)
= \(\dfrac{320}{16}\) : 2
= 320 : 16 : 2 ( đpcm)
câu 1 B
câu 2 D
câu 3 ko bt
câu 4 x=-1/2; x = -(căn bậc hai(3)*i-1)/4;x = (căn bậc hai(3)*i+1)/4;
câu 5 x=-5/3, x=0, x=1
Câu 1: x2 + 2 xy + y2 bằng:
A. x2 + y2 B.(x + y)2 C. y2 – x2 D. x2 – y2
Câu 2: (4x + 2)(4x – 2) bằng:
A. 4x2 + 4 B. 4x2 – 4 C. 16x2 + 4 D. 16x2 – 4
Câu 3: 25a2 + 9b2 - 30ab bằng:
A.(5a-9b)2 B.(5a – 3b)2 C.(5a+3b)2 D.(5a)2 – (3b)2
Câu 4: 8x3 +1 bằng
A.(2x+1).(4x2-2x+1) B. (2x-1).(4x2+2x+1) C.(2x+1)3 D.(2x)3-13
Câu 5:Thực hiện phép nhân x(3x2 + 2x - 5) ta được:
A.3x3 - 2x2 – 5x B. 3x3 + 2x2 – 5x C. 3x3 - 2x2 +5x D. 3x3 + 2x2 + 5x
`4-x=2(x-4)^2`
`<=>4-x=2(x^2-8x+16)`
`<=> 4-x=2x^2 - 16x+32`
`<=> 4-x-2x^2+16x-32=0`
`<=> -2x^2 +15x-28=0`
`<=> -(2x^2-15x+28)=0`
`<=>-(2x^2-7x-8x+28)=0`
`<=> - [x(2x-7) - 4(2x-7)]=0`
`<=> -(2x-7)(x-4)=0`
\(\Leftrightarrow\left[{}\begin{matrix}-2x+7=0\\x-4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}-2x=-7\\x=4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=4\end{matrix}\right.\)
__
`(x^2 +1) (x-2)+2x=4`
`<=> x^3 -2x^2 +x-2+2x-4=0`
`<=> x^3 -2x^2 +3x-6=0`
`<=> (x^3+3x)-(2x^2+6)=0`
`<=> x(x^2 +3) -2(x^2+3)=0`
`<=>(x^2+3)(x-2)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x^2+3=0\\x-2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x\in\varnothing\\x=2\end{matrix}\right.\)
__
`x^4 -16x^2=0`
`<=> x^2 (x^2 -16)=0`
`<=>x^2(x-4)(x+4)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\x-4=0\\x+4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
\(4-x=2\left(x-4\right)^2\)
\(\Leftrightarrow4-x=2\left(x^2-8x+16\right)\)
\(\Leftrightarrow4-x=2x^2-16x+32\)
\(\Leftrightarrow2x^2-15x+28=0\)
\(\Leftrightarrow2x^2-7x-8x+28=0\)
\(\Leftrightarrow x\left(2x-7\right)-4\left(2x-7\right)=0\)
\(\Leftrightarrow\left(2x-7\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-7\\x=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=4\end{matrix}\right.\)
___________
\(\left(x^2+1\right)\left(x-2\right)+2x=4\)
\(\Leftrightarrow x^3-2x^2+x-2+2x=4\)
\(\Leftrightarrow x^3-2x^2+3x-2-4=0\)
\(\Leftrightarrow x^3-2x^2+3x-6=0\)
\(\Leftrightarrow x^2\left(x-2\right)+3\left(x-2\right)=0\)
\(\Leftrightarrow\left(x^2+3\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=-3\left(\text{vô lý}\right)\\x=2\left(tm\right)\end{matrix}\right.\)
\(\Leftrightarrow x=2\)
________________
\(x^4-16x^2=0\)
\(\Leftrightarrow\left(x^2\right)^2-\left(4x\right)^2=0\)
\(\Leftrightarrow\left(x^2-4x\right)\left(x^2+4x\right)=0\)
\(\Leftrightarrow x\left(x-4\right)x\left(x+4\right)=0\)
\(\Leftrightarrow x^2\left(x-4\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\x-4=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
\(\left(x-y\right)^2-4=\left(x-y-2\right)\left(x-y+2\right)\)
\(9-\left(x-y\right)^2=\left(3-x+y\right)\left(3+x-y\right)\)
\(\left(x^2+4\right)^2-16x^2=\left(x^2-4x+4\right)\left(x^2+4x+4\right)=\left(x-2\right)^2\left(x+2\right)^2\)
\(a,=5\left(x^3+8y\right)\\ b,=\left(4x+y\right)^2-16=\left(4x+y-4\right)\left(4x+y+4\right)\\ c,=3\left(x^2+2\cdot\dfrac{7}{3}x-5\right)\\ =3\left(x^2+2\cdot\dfrac{7}{3}x+\dfrac{49}{9}-\dfrac{94}{9}\right)\\ =3\left(x+\dfrac{7}{3}-\dfrac{\sqrt{94}}{3}\right)\left(x+\dfrac{7}{3}+\dfrac{\sqrt{94}}{3}\right)\)
a: \(5x^3+40y=5\left(x^3+8y\right)\)
b: \(16x^2+8xy+y^2-16\)
\(=\left(4x+y\right)^2-16\)
\(=\left(4x+y-4\right)\left(4x+y+4\right)\)
1)
x^3 -16x=0`
`<=>x(x^2 -16)=0`
\(< =>\left[{}\begin{matrix}x=0\\x^2-16=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=0\\x^2=16\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
b)
`x^4 -2x^3=0`
`<=>x^3 (x-2)=0`
\(< =>\left[{}\begin{matrix}x^3=0\\x-2=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)
3)
`(2x-11)(x^2 -1)=0`
\(< =>\left[{}\begin{matrix}2x-11=0\\x^2-1=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}2x=11\\x^2=1\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=\dfrac{11}{2}\\x=1\\x=-1\end{matrix}\right.\)
4)
`x^3 -36x=0`
`<=>x(x^2 -36)=0`
\(< =>\left[{}\begin{matrix}x=0\\x^2-36=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=0\\x^2=36\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=0\\x=6\\x=-6\end{matrix}\right.\)
5)
`2x+19=0`
`<=>2x=-19`
`<=>x=-19/2`
(4x16)+(16x2)
= 64 + 32
= 96