Bài 3: Những hằng đẳng thức đáng nhớ
Các câu hỏi tương tự
Cho biểu thức A=\(\dfrac{x^2}{\left(x+y\right)\left(1-y\right)}-\dfrac{y^2}{\left(x+y\right)\left(1+x\right)}-\dfrac{x^2y^2}{\left(1+x\right)\left(1-y\right)}\)
a) Rút gọn A
b) Tính các cặp gia trị nguyên (x.y)để A=-3
Cho biểu thức A=\(\dfrac{x^2}{\left(x+y\right)\left(1-y\right)}-\dfrac{y^2}{\left(x+y\right)\left(1+x\right)}-\dfrac{x^2y^2}{\left(1+x\right)\left(1-y\right)}\)
a) Rút gọn A
b) Tính các cặp gia trị nguyên (x.y)để A=-3
1) Cho a^2+b^2+c^2+32left(a+b+cright)
CMR: abc1
2) CMR: nếu left(a^2+b^2right)left(x^2+y^2right)left(ax+byright)^2 thì dfrac{a}{x}dfrac{b}{y}
3) Cho left(a^2+b^2+c^2right)left(x^2+y^2+z^2right)left(ax+by+czright)^2
CMR: dfrac{a}{x}dfrac{b}{y}dfrac{c}{z}
Đọc tiếp
1) Cho \(a^2+b^2+c^2+3=2\left(a+b+c\right)\)
CMR: \(a=b=c=1\)
2) CMR: nếu \(\left(a^2+b^2\right)\left(x^2+y^2\right)=\left(ax+by\right)^2\) thì \(\dfrac{a}{x}=\dfrac{b}{y}\)
3) Cho \(\left(a^2+b^2+c^2\right)\left(x^2+y^2+z^2\right)=\left(ax+by+cz\right)^2\)
CMR: \(\dfrac{a}{x}=\dfrac{b}{y}=\dfrac{c}{z}\)
1. tính
a) left(dfrac{2}{3}x-dfrac{3}{2}yright)^2
b) left(dfrac{1}{2}x^2+dfrac{1}{3}right)^2
c) left(x+dfrac{1}{5}y^2right)left(x-dfrac{1}{5}y^2right)
d) left(dfrac{1}{2}x-2yright)^3
e) left(-dfrac{1}{2}xy^2+xright)^3
f) 27x^3-8y^3
g) 4(2x - 3y) - 4 - (2x-3y)2
2. rút gọn
a) 2mleft(5m+2right)+left(2m-3right)left(3m-1right)
b) left(2x+4right)left(8x-3right)-left(4x+1right)^2
c) left(7y-2right)^2-left(7y+1right)left(7y-1right)
d) left(a+2right)^3-aleft(a-3right)^2
3. c/...
Đọc tiếp
1. tính
a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\)
b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\)
c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\)
d) \(\left(\dfrac{1}{2}x-2y\right)^3\)
e) \(\left(-\dfrac{1}{2}xy^2+x\right)^3\)
f) \(27x^3-8y^3\)
g) 4(2x - 3y) - 4 - (2x-3y)2
2. rút gọn
a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\)
b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\)
c) \(\left(7y-2\right)^2-\left(7y+1\right)\left(7y-1\right)\)
d) \(\left(a+2\right)^3-a\left(a-3\right)^2\)
3. c/m các biểu thức sau ko phụ thuộc vào biến x,y
a) \(\left(2x-5\right)\left(2x+5\right)-\left(2x-3\right)^2-12x\)
b) \(\left(2y-1\right)^3-2y\left(2y-3\right)^2-6y\left(2y-2\right)\)
c) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(20+x^3\right)\)
d) \(3y\left(-3y-2\right)^2-\left(3y-1\right)\left(9y^2+3y+1\right)-\left(-6y-1\right)^2\)
4. Tìm x
a) \(\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\)
b) \(\left(8x^2+3\right)\left(8x^2-3\right)-\left(8x^2-1\right)^2=22\)
c) \(49x^2+14x+1=0\)
d) \(\left(x-1\right)^3-x\left(x-2\right)^2-\left(x-2\right)=0\)
5. c/m biểu thức luôn dương:
a) \(A=16x^2+8x+3\)
b) \(B=y^2-5y+8\)
c) C= \(2x^2-2x+2\)
d) \(D=9x^2-6x+25y^2+10y+4\)
6. Tìm GTLN và GTNN của các biểu thức sau
a) \(M=x^2+6x-1\)
b) \(N=10y-5y^2-3\)
7. thu gọn
a) \(\left(2+1\right)\left(2^2+1\right)\left(2^3+1\right)...\left(2^{32}+1\right)-2^{64}\)
b) \(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{\text{64}}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)
Rút gọn biểu thức:
a) Aleft(x-yright)^3+left(y+xright)^3+left(y-xright)^3-3xyleft(x+yright)
b) B3x^2left(x+1right)left(x-1right)-left(x^2-1right)left(x^4+x^2+1right)+left(x^2-1right)^3
c) Cleft(x+yright)left(x^2-xy+y^2right)+left(x-yright)left(x^2+xy+y^2right)-2x^3
d) Dleft(x+1right)^3+left(x-1right)^3+x^3-3xleft(x+1right)left(x-1right)
Đọc tiếp
Rút gọn biểu thức:
a) \(A=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)
b) \(B=3x^2\left(x+1\right)\left(x-1\right)-\left(x^2-1\right)\left(x^4+x^2+1\right)+\left(x^2-1\right)^3\)
c) \(C=\left(x+y\right)\left(x^2-xy+y^2\right)+\left(x-y\right)\left(x^2+xy+y^2\right)-2x^3\)
d) \(D=\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)
1.Chứng minh các đăngr thức sau
a) \(\dfrac{\left(a+b\right)^2-\left(a-b\right)^2}{4}=ab\)\(\)
b) \(2\left(x^2+y^2\right)=\left(x+y\right)^2+\left(x-y\right)^2\)
Rút gọn các biểu thức:
a, \(\left(x+1\right)-\left(x-4\right)^2-3\left(x+1\right)\left(x-2\right)\)
b, \(5\left(x+2\right)\left(x-2\right).2\dfrac{1}{2}\left(6-8x\right)^2+17\)
Tìm x :
a, \(\left(2x+1\right)^2-3x^2+4=\left(1-x\right).\left(1+x\right)\)
b, \(\left(4x-3\right)\cdot\left(4x+3\right)-2\cdot\left(x+2\right)^2=14x^2\)
c, \(\left(2x-1\right)\cdot\left(x+1\right)-x^2+1=\dfrac{1}{2}\cdot\left(x-1\right)^2\)
Bài 1: Tìm x
a) left(5-2xright)^2-160
b) x^2-4x29
c) left(x-3right)^3-left(x-3right).left(x^2+3x+9right)+9.left(x+1right)^215
d) 2.left(x-5right).left(x+5right)-left(x+2right).left(2x-3right)+x.left(x^2-8right)left(x+1right).left(x^2-x+1right)
Bài 2: Rút gọn
a) left(x^2+x+1right).left(x^2-x+1right).left(x^2-1right)
b) left(a+b-cright)^2+left(a-b+cright)^2-2.left(b-cright)^2
c) left(a+b+cright)^2-left(a+bright)^2-left(a+cright)^2-left(b+cright)^2
d) left(a+b+cright)^2+left(a-b-cright)^2+...
Đọc tiếp
Bài 1: Tìm x
a) \(\left(5-2x\right)^2-16=0\)
b) \(x^2-4x=29\)
c) \(\left(x-3\right)^3-\left(x-3\right).\left(x^2+3x+9\right)+9.\left(x+1\right)^2=15\)
d) \(2.\left(x-5\right).\left(x+5\right)-\left(x+2\right).\left(2x-3\right)+x.\left(x^2-8\right)=\left(x+1\right).\left(x^2-x+1\right)\)
Bài 2: Rút gọn
a) \(\left(x^2+x+1\right).\left(x^2-x+1\right).\left(x^2-1\right)\)
b) \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2.\left(b-c\right)^2\)
c) \(\left(a+b+c\right)^2-\left(a+b\right)^2-\left(a+c\right)^2-\left(b+c\right)^2\)
d) \(\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)