Tìm GTNN :
A=5x2+2y2+2xy−26x−16y+54A=5x^2+2y^2+2xy-26x-16y+54A=5x2+2y2+2xy−26x−16y+54
B=(x+2y)2+(x−4)2+(y−1)2−27B=\left(x+2y\right)^2+\left(x-4\right)^2+\left(y-1\right)^2-27B=(x+2y)2+(x−4)2+(y−1)2−27
câu B tương tự thui bạn:))) B=(x+2y)2+(x−4)2+(y−1)2−27B=\left(x+2y\right)^2+\left(x-4\right)^2+\left(y-1\right)^2-27B=(x+2y)2+(x−4)2+(y−1)2−27
=2x2+4xy+5y2−8x−2y−10=2x^2+4xy+5y^2-8x-2y-10=2x2+4xy+5y2−8x−2y−10
=2(x2+2x(y−2)+(y−2)2)−2(y−2)2+5y2−2y+10=2\left(x^2+2x\left(y-2\right)+\left(y-2\right)^2\right)-2\left(y-2\right)^2+5y^2-2y+10=2(x2+2x(y−2)+(y−2)2)−2(y−2)2+5y2−2y+10
=2(x+(y−2))2+3y2+6y−18=2\left(x+\left(y-2\right)\right)^2+3y^2+6y-18=2(x+(y−2))2+3y2+6y−18
=2(x+y−2)2+3(y+1)2−21≥−21=2\left(x+y-2\right)^2+3\left(y+1\right)^2-21\ge-21=2(x+y−2)2+3(y+1)2−21≥−21
Dấu '' = '' xảy ra khi ⇔{y+1=0x+y−2=0⇔{x=3y=−1\Leftrightarrow\left\{{}\begin{matrix}y+1=0\\x+y-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-1\end{matrix}\right.⇔{y+1=0x+y−2=0⇔{x=3y=−1
Vậy: Min B = -21 tại x=3;y=−1.x=3;y=-1.x=3;y=−1.
Áp dụng lập phương của 1 tổng
Tính:
a) (2x2+3y)3\left(2x^2+3y\right)^3(2x2+3y)3
b) (12x−3)3\left(\dfrac{1}{2}x-3\right)^3(21x−3)3
Cho a+b+c=0. Chứng minh a4+b4+c4 bằng mỗi biểu thức:
a, 2(a2b2 + b2c2 + c2a2) b, 2(ab+bc+ca)2 c, (a2+b2+c2)2\dfrac{\left(a^2+b^2+c^2\right)}{2}2(a2+b2+c2)
Cho x - y = 2. Tính:
B = 2 × ( x^3 - y^3 ) - 3 × ( x + y )^2
PTĐTTNT
(x+2)(x+3)(x+4)(x+5)-24
cho x + y = 5 tính 3x2−2x+3y2−2y+6xy−1003x^2-2x+3y^2-2y+6xy-1003x2−2x+3y2−2y+6xy−100
Viết các biểu thức sau dưới dạng bình phương của một tổng hoặc hiệu
a) x2+4x+4x^2+4x+4x2+4x+4
b) 16x2−8xy+y216x^2-8xy+y^216x2−8xy+y2
c) 9a2+16b2−24ab9a^2+16b^2-24ab9a2+16b2−24ab
d) x2−x+14x^2-x+\dfrac{1}{4}x2−x+41
e) y2+12y+116y^2+\dfrac{1}{2}y+\dfrac{1}{16}y2+21y+161
X4+y4+(x+y)4=2(x2+xy+y2)2X^4+y^4+\left(x+y\right)^4=2\left(x^2+xy+y^2\right)^2X4+y4+(x+y)4=2(x2+xy+y2)2Chứng minh hàng đẳng thức
Cho x2+y2=1. Chứng minh rằng: (x+y)2≤\le≤2.
Giúp mk với, mới mk nộp rồi
1) Cho x + y = 5. Tính:
P=3x2−2x+3y2−2y+6xy−100Q=x3+y3−2x2−2y2+3xy(x+y)−4xy+3(x+y)+10P=3x^2-2x+3y^2-2y+6xy-100\\ Q=x^3+y^3-2x^2-2y^2+3xy\left(x+y\right)-4xy+3\left(x+y\right)+10P=3x2−2x+3y2−2y+6xy−100Q=x3+y3−2x2−2y2+3xy(x+y)−4xy+3(x+y)+10
502-492+482-472+462-452-.+22-12
