1: \(A=11-\left|x-1\right|-\left(y-1\right)^2< =11\)
Dấu '=' xảy ra khi x=1 và y=1
3: \(C=\left|x-1\right|-\left|2018-x\right|\le\left|x-1+2018-x\right|=2017\)
Dấu '=' xảy ra khi x-1>0 và 2018-x<0
=>x>2018
1, Chứng minh các biểu thức sau không phụ thuộc vào biến :
\(A=\left(x+3\right)^3-\left(x+9\right).\left(x^2-27\right)\)
\(B=\left(x+y\right).\left(x^2-x.y+y^2\right)+\left(x-y\right).\left(x^2+x.y+y^2\right)-2.\left(x^3-9\right)\)
2, Cho \(\left(a^2+b^2\right).\left(x^2-y^2\right)=\left(ã.+b.y\right)\)
CMR : \(\frac{a}{x}=\frac{b}{y}\)
Tìm GTLN
a, P = -\(\left|x-2\right|\) - 1
b, E = 1 - ( x - 1 )2
c, G = - ( -x + 2 )2 + 3
d, A = \(\left|x-1\right|\) - \(\left|x-2\right|\)
Tìm x biết
a, 15 - ( x - 2 ) + 27 = -13
b, ( 5 - x ) - 12 = -114
c, \(\left|x\right|\) + 5 = -10 + 9
d, \(\left|x-3\right|\) = -12 + 15
e, \(\left|x-1\right|\) = \(\left|-2018+7\right|\)
g, \(\left|x-1\right|\) = \(\left|2x+3\right|\)
Bài 1: Tìm x, y biết:
a) \(\left(3-2x\right)^2+\left(y-5\right)^{20}\le0\)
b) \(\left(2x-1\right)\left(x+2\right)\ge0\)
c) \(\left(x-3\right)\left(x-4\right)\le0\)
d) \(x^2-7x\le0\)
e) \(x^2+4x\ge0\)
Bài 2: Tìm x,y nguyên biết:
a) \(y^2-3xy-1=0\)
b) \(y^2-4xy-5=1\)
c) \(\left(x-12\right)\left(y+5\right)=7\)
d) \(xy-2x+3y=8\)
e) \(2xy-3x+y-3=5\)
Tìm GTNN của
a, A = \(\left|x-2\right|\) + y2 = 5
b, B = \(\left|x-2\right|\) - 1
c, C = 2 . \(\left|1-x\right|\) + 1
Tìm GTTNN của
1, A = \(\left|x-1\right|\) + 15
2, B = 2 + ( x - 1 )2
3, C = \(\left|x-1\right|\) + \(\left|x-2\right|\)
Tìm GTLN
A= \(\left|x-1\right|\) - \(\left|x-2\right|\)
a) \(1-\left(5\frac{3}{8}+x-7\frac{5}{24}\right):\left(-16\frac{2}{3}\right)=0\)
b) \(\left(\frac{x}{3}-5\frac{1}{4}\right)^2-\frac{-2}{5}=1\frac{1}{25}\)
c) \(\frac{17-x}{12}=\frac{3}{17-x}\)
d) \(1\frac{1}{3}-25\%\left(x-\frac{8}{3}\right)+2x=1,6:\frac{3}{5}\)
tìm x
a,\(\dfrac{6}{7}-\dfrac{3}{4}x=-1\dfrac{1}{2}x-3\)
b\(\left(4x-1\right)^2=\left(4x-1\right)^4\)
c\(\left(\dfrac{4}{5}-\dfrac{3}{4}:x\right)^3=\dfrac{-1}{27}\)
d\(\left|\dfrac{4}{3}-\dfrac{1}{4}x\right|:2\dfrac{1}{3}=0,5\)
giúp mình nhé
