Tính:
\(\left[\left(a-b\right)^3+2\left(a-b\right)^2\right]:\left(b-a\right)^2\)
Ai nhanh nhất mk tjck cho nhá!
\(\left[5\left(a-b\right)^3+2\left(a-b\right)^2\right]:\left(b-a\right)^2\)
Nhanh nhất mk tjck cho!^_^
đk: a khác b.
\(=\frac{\left(a-b\right)^2\left(5\left(a-b\right)+2\right)}{\left(a-b\right)^2}=5a-5b+2\)
Theo mk là vầy các pn xem dc k nka!
\(\left[5\left(a-b\right)^3+2\left(a-b\right)^2\right]:\left(b-a\right)^2\)
\(=\left[5\left(a-b\right)^3+2\left(a-b\right)^2\right]:\left(a-b\right)^2\)
\(=5\left(a-b\right)+2\)
Cho M= \(\left(x-a\right)\left(x-b\right)+\left(x-b\right)\left(x-c\right)+x^2\)
M the a,b,c biết \(x=\dfrac{1}{2}a+\dfrac{1}{2}b+\dfrac{1}{2}c\)
Ai giups mk vs ai nhanh mk sẽ vote nha
Từ x=\(\dfrac{1}{2}\)a+\(\dfrac{1}{2}\)b+\(\dfrac{1}{2}\)c=\(\dfrac{1}{2}\).(a+b+c)\(\Rightarrow\)2x=(a+b+c)
M=(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)+x\(^2\)
= x\(^2\)-xb-ax+ab+x\(^2\)-xc-bx+bc+x\(^2\)-ax-cx+ac+x\(^2\)
= 4x\(^2\)-2ac-2bx-2cx+ab+bc+ac
= 4x\(^2\)-2x(a+b+c)+ab+bc+ca
Thay 2x=a+b+c,ta được:
M= 4x\(^2\)-2x.2c+ab+bc+ca
M= 4x\(^2\)-4x\(^2\)+ab+bc+ca
M= ab+bc+ca
Tìm GTNN của
a/A=\(a^2+5b^2-4ab-2b+5\)
b/B=\(\left(x-y\right)^2+\left(y-3^{ }\right)^2+\left(x-3\right)^2+2021\)
Ai giúp mk vs ạ ai nhanh mk tick nha :3
b: \(B\ge2021\forall x,y\)
Dấu '=' xảy ra khi x=y=3
Tính giá trị biểu thức:
\(B=\left(-1\right)\left(-1\right)^2\left(-1\right)^3\left(-1\right)^4...\left(-1\right)^{2014}\)
Làm nhanh hộ mk nhé,mk cần gấp
Ai làm nhanh nhất mk sẽ like cho
\(\Rightarrow B=-1.-1^3.....-1^{2013}\left(-1^{2x}=1\right).\)
\(=-1^{1008}\)
= 1
\(B=\left(-1\right)\left(-1\right)^2\left(-1\right)^3\left(-1\right)^4...\left(-1\right)^{2014}\)
\(\Rightarrow B=\left(-1\right)^1\left(-1\right)^2\left(-1\right)^3\left(-1\right)^4...\left(-1\right)^{2014}\)
\(\Rightarrow B=\left(-1\right)^{1+2+3+4+...+2014}\)
\(\Rightarrow B=\left(-1\right)^{2029105}\)
\(\Rightarrow B=-1\)
Rút gọn :
\(a,A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\\ b,B=-1^2+2^2-3^2+4^2-...-99^2+100^2\\ c,C=-1^2+2^2-3^2+4^2-...+\left(-1\right)^n\cdot n^2\\ d,D=3\cdot\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\\ e,E=\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\\ g,G=\left(a+b+c+d\right)^2+\left(a+b-c-d\right)^2+\left(a+c-b-d\right)^2+\left(a+d-b-c\right)^2\\ h,H=\left(a+b+c\right)^3-\left(b+c-a\right)^3-\left(a+c-b\right)^3+\left(a+b-c\right)^3\\ i,I=\left(a+b\right)^3+\left(b+c\right)^3+\left(c+a\right)^3-3\left(a+b\right)\left(c+b\right)\left(c+a\right)\)
Mọi người ơi, giúp mk vs, đc câu nào hay câu ấy ! Help me!!!!!!!!!!!!!!!!!!
a/ \(A=\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(2A=2\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(2A=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(2A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(2A=\left(3^4-1\right)\left(3^4+1\right)...\left(3^{64}+1\right)\)
\(\Rightarrow2A=3^{128}-1\Rightarrow A=\dfrac{3^{128}-1}{2}\)
e) ta dể dàng thấy được : \(a^2+b^2=\left(a+b\right)^2-2ab\)
\(\Rightarrow E=\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)
\(=\left(2a+2b\right)^2-2\left(a+b+c\right)\left(a+b-c\right)-2\left(a+b\right)^2\)
\(=4\left(a+b\right)^2-2\left(\left(a+b\right)^2-c^2\right)-2\left(a+b\right)^2\)
\(=4\left(a+b\right)^2-2\left(a+b\right)^2+2c^2-2\left(a+b\right)^2=2c^2\)
g) củng sử dụng cái trên ta có : \(G=\left(a+b+c+d\right)^2+\left(a+b-c-d\right)^2+\left(a+c-b-d\right)^2+\left(a+d-b-c\right)^2\)
\(=\left(2a+2b\right)^2-2\left(a+b+c+d\right)\left(a+b-c-d\right)+\left(2a-2b\right)^2-2\left(a+c-b-d\right)\left(a+d-b-c\right)\)
\(=4\left(a+b\right)^2+4\left(a-b\right)^2-2\left(\left(a+b\right)^2-\left(c+d\right)^2\right)-2\left(\left(a-b\right)^2-\left(c-d\right)^2\right)\)
\(=4\left(\left(a+b\right)^2+\left(a-b\right)^2\right)-2\left(\left(a+b\right)^2+\left(a-b\right)^2\right)+2\left(\left(c+d\right)^2+\left(c-d\right)^2\right)\)
\(=2\left(\left(a+b\right)^2+\left(a-b\right)^2\right)+2\left(\left(c+d\right)^2+\left(c-d\right)^2\right)\)\(=2\left(\left(2a\right)^2-2\left(a+b\right)\left(a-b\right)\right)+2\left(\left(2c\right)^2-2\left(c+d\right)\left(c-d\right)\right)\)
\(=2\left(4a^2-2\left(a^2-b^2\right)\right)+2\left(4c^2-2\left(c^2-d^2\right)\right)\)
\(=2\left(2a^2+2b^2\right)+2\left(2c^2+2d^2\right)=4\left(a^2+b^2+c^2+d^2\right)\)
bn đăng nhiều quá nên mk làm câu nào hay câu đó nha
mà nè mấy câu a;b;c;d hình như trên mạng có bn lên đó tìm nha .
Bài 1: Cho \(\left|a-c\right|< 3,\left|b-c\right|< 2\). Chứng minh \(\left|a-b\right|< 5\)
Giúp mk vs, ai nhanh mk sẽ tick
Phân tích đa thức sau thành nhân tử: \(a^3\left(c-b^2\right)+b^3\left(a-c^2\right)+c^3\left(b-a^2\right)+abc\left(abc-1\right).\)
Ai làm nhanh, đầy đủ và đúng nhất mình sẽ tick! ^_^
a^3(c−b^2)+b^3(a−c^2)+c^3(b−a^2)+abc(abc−1)
=a^3c−a^3b^2+b^3(a−c^2)+bc^3−a^2c^3+a^2b^2c^2−abc
=(a^3c−a^2c^3)+b^3(a−c^2)−(a^3b^2−a^2b^2c^2)+(bc^3−abc)
=a^2c(a−c^2)+b^3(a−c^2)−a^2b^2(a−c^2)−bc(a−c^2)
=(a^2c+b^3−a^2b^2−bc)(a−c2)
=[c(a^2−b)−b^2(a^2−b)](a−c^2)=(a^2-b)(c-b^2)(a-c^2)
5) Tính
a) \(4.\left(1\frac{1}{4}\right)^2+25.[\left(\frac{3}{4}\right)^2:\left(\frac{5}{4}\right)^3]:\left(\frac{3}{2}\right)^3\)
b) \(3-\left(\frac{-6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2\)
MK CẦN GẤP Ạ , AI NHANH MK TICK NHÉ , CẢM ƠN TRƯỚC
\(\left(a+b+c+d\right)^2+\left(a+b-c-d\right)^2+\left(a+c-b-d\right)^2+\left(a+d-b-c\right)^2.\)
Ai biết thì làm giúp mình nha, mình cần gấp lắm, ai làm nhanh nhất mình k nha!