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a) 4x^2(5x^3 - 2x + 3)
= 20x^5 - 8x^3 + 12x^2
b) 2u(1 + u - v) - v(1 - 2u + v)
= 2u + 2u^2 - v - v^2
a) 3 u 2 − 8 u + 3 ( u 2 + 1 ) ( u − 1 ) b) 1 − 4 u 4 ( 4 u + 1 )
a, \(x^2+2x\left(y+1\right)+y^2+2y+1=\left(x^2+2xy+y^2\right)+\left(2x+2y\right)+1\)
\(=\left(x+y\right)^2+2\left(x+y\right)+1=\left(x+y+1\right)^2\)
b, \(u^2+v^2+2u+2v+2\left(u+1\right)\left(v+1\right)+2\)
\(=u^2+v^2+2u+2v+2uv+2u+2v+2+2\)
\(=\left(u^2+2uv+v^2\right)+\left(4u+4v\right)+4\)
\(=\left(u+v\right)^2+4\left(u+v\right)+2^2=\left(u+v+2\right)^2\)
1.
a) \(A=x^2+2x\left(y+1\right)+y^2+2y+1\)
\(A=x^2+2x\left(y+1\right)+\left(y+1\right)^2\)
\(A=\left(x+y+1\right)^2\)
b) \(B=u^2+v^2+2u+2v+2\left(u+1\right)\left(v+1\right)+2\)\(B=u^2+v^2+2u+2v+2\left(u+1\right)\left(v+1\right)+1+1\)\(B=\left(u^2+2u+1\right)+2\left(u+1\right)\left(v+1\right)+\left(v^2+2v+1\right)\)\(B=\left(u+1\right)^2+2\left(u+1\right)\left(v+1\right)+\left(v+1\right)^2\)\(B=\left(u+1+v+1\right)^2=\left(u+v+2\right)^2\)
tik mik nha !!!
a.) \(A=x^2+y^2+1+2xy+2x+2y=\left(x+y+1\right)^2.\)
b.) \(B=u^2+v^2+2u+2v+2\left(u+1\right)\left(v+1\right)+2=u^2+2u+1+2\left(u+1\right)\left(v+1\right)+v^2+2v+1\)
\(B=\left(u+1\right)^2+2\left(u+1\right)\left(v+1\right)+\left(v+1\right)^2=\left(u+1+v+1\right)^2=\left(u+v+2\right)^2\)
Giả sử số tự nhiên a chia cho 7 dư 3. CMR a chia cho 7 dư 2
a) Đặt A = u2 + v2 - 2u + 3v + 15
= (u2 - 2u + 1) + (v2 + 3v + 9/4) + 47/4
= (u - 1)2 + (v + 3/2)2 + 47/4 \(\ge\frac{47}{4}\)
Dấu "=" xảy ra <=> \(\hept{\begin{cases}u-1=0\\v+\frac{3}{2}=0\end{cases}}\Rightarrow\hept{\begin{cases}u=1\\v=-\frac{3}{2}\end{cases}}\)
Vậy Min A = 47/4 <=> u = 1 ; y = -3/2
(u-1)^2 + (v+3/2)^2 + 11,75 \(\ge\)11,75
''='' <=> u = 1, v = -3/2
=> Min = 11,75 <=> u = 1, v = -3/2
Giải:
Ta có: \(U_{n-1}=\dfrac{3U_n-U_{n+1}}{2}\) nên:
\(U_4=340;U_3=216;U_2=154;U_1=123\)
Từ \(U_5=588;U_6=1084;U_{n+1}=3U_n-2U_{n-1}\)
\(\Rightarrow\) \(U_{25}=520093788\)
Vậy \(U_2=154;U_1=123;\) \(U_{25}=520093788\)
bn lấy y ở đâu ra thế?