a ) \(\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x+7\right)\left(x-7\right)=24\)
\(\Leftrightarrow4x^2-4x+1+x^2+6x+9-5x^2+245=24\)
\(\Leftrightarrow2x=-231\Leftrightarrow x=\dfrac{-231}{2}\)
b ) \(\left(x+3\right)^2-\left(x-4\right)\left(x-8\right)=1\)
\(\Leftrightarrow x^2+6x+9-x^2+12x-32=1\)
\(\Leftrightarrow18x=24\Leftrightarrow x=\dfrac{4}{3}\)
Chúc bạn học tốt !!!!!!!!!!!!
Bài 1: Cm giá trị của biểu thức sau không phụ thuộc vào biến x:
a) \(\left(2x+3\right).\left(4x^2-6x+9\right)-2\left(4x^3-1\right)\)
b)\(\left(x+3\right)^3+\left(x+9\right).\left(x^2+27\right)\)
c)\(\left(x+y\right).\left(x^2-xy+y^2\right)+\left(x-y\right).\left(x^2+xy+y^2\right)-2x^3\)
Bài 2: Tìm x biết:
a) \(\left(x+2\right)^2-9=0\)
b) \(\left(x+2\right)^2-x^2+4=0\)
c) \(\left(x-3\right)^2-4=0\)
d) \(x^2-2x=24\)
e) \(\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x-7\right)\left(x+7\right)=0\)
Tìm x biết :
a, \(\left(x-1\right)^2-\left(x+3\right)\left(x-3\right)=5\)
b, \(\left(x+3\right)^2-x\left(x-1\right)=6\)
c, \(\left(x-1\right)\left(x^2+x+1\right)+\left(2x\right)\left(4-2x+x2\right)=5-x\)
Tìm x:
\(1,\left(3x-5\right)^2-\left(3x+1\right)^2=8\)
2,\(2x.\left(8x-3\right)-\left(4x-3\right)^2=27\)
3,\(\left(2x-3\right)^2-\left(2x+1\right)^2=3\)
4, \(\left(x+5\right)^2-x^2=45\)
5, \(\left(x-3\right)^3-\left(x-3\right).\left(x^2+3x+9\right)+9.\left(x+1\right)^2=18\)
6,\(x.\left(x-4\right).\left(x+4\right)-\left(x-5\right).\left(x^2+5x+25\right)=13\)
tìm x biết
a)\(\left(x-2\right)^2-x\left(x+1\right)\left(x-1\right)+6x\left(x-3\right)=0\)
b)\(\left(x-2\right)\left(x^2-2x+4\right)\left(x+2\right)\left(x^2+2x+4\right)-x^6+2x=1\)
c)\(\left(x-3\right)\left(x^2+3x+9\right)+x\left(x+2\right)\left(2-x\right)=1\)
Tìm x, biết:
a. \(\left(2x-3\right)^2-4=0\)
b.\(x^2-2x=0\)
c.\(\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x+7\right)\left(x-7\right)=0\)
1) Tìm x biết,
\(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)=11\)
2) Rút gọn các biểu thức
a) \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
b) \(\left(a-b+c\right)^2-\left(b-c\right)^2+2ab-2ac\)
c) \(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)
d) \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
e) \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)
3) Chứng minh rằng các biểu thức sau luôn luôn có giá trị dương với mọi giá trị của biến
a) \(9x^2-6x+2\)
b) \(x^2+x+1\)
c) \(2x^2+2x+1\)
4) Tìm GTNN của các biểu thức
a) A=\(x^2-3x+5\)
b) B=\(\left(2x-1\right)^2+\left(x+2\right)^2\)
GIÚP MK VỚI!!!!!!!!!!
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) \(\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)
Dùng hằng đẳng thức để triển khai và thu gọn:
a) \(x\left(x-1\right).\left(x+1\right)-\left(x+1\right)\left(x^2-x+1\right)\)
b) \(\left(x-1\right)^3-\left(x+2\right).\left(x^2-2x+4\right)+3.\left(x+4\right).\left(x-4\right)\)
c) \(3x^2.\left(x+1\right).\left(x-1\right)+\left(x^2-1\right)^3-\left(x^2-1\right).\left(x^4+x^2+1\right)\)
Rút gọn rồi tính giá trị biểu thức :
a) \(A=\left(x+3\right)^2+\left(x-3\right).\left(x+3\right)-2.\left(x+2\right).\left(x-4\right)\); với x = \(-\frac{1}{2}\)
b) \(B=\left(3x+4\right)^2-\left(x-4\right).\left(x+4\right)-10x\); với x = \(-\frac{1}{10}\)
c) \(C=\left(x+1\right)^2-\left(2x-1\right)^2+3.\left(x-2\right).\left(x+2\right)\); với x = 1
d) \(D=\left(x-3\right).\left(x+3\right)+\left(x-2\right)^2-2x.\left(x-4\right)\); với x = -1
