Áp dụng \(x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)\)
Ta có \(P=\left(x^2\right)^3+\left(y^2\right)^3=\left(x^2+y^2\right)^3-3x^2y^2\left(x^2+y^2\right)\)
\(\Rightarrow P=1-3x^2y^2\ge1-3\dfrac{\left(x^2+y^2\right)^2}{4}=\dfrac{1}{4}\)
\(\Rightarrow P_{min}=\dfrac{1}{4}\) khi \(x^2=y^2=\dfrac{1}{2}\)
cho 2 so x, y thoa man: x2+x2y2-2y=0 va x3+ 2y2-4y+3=0
tinh gia tri cua bieu thuc Q=x2+y2
Tim gia tri nho nhat :
P=(2x+1/x)2+(2y+1/y)2
Gia tri cua y thoa man :
\(x^2-6x+y^2+10y+34=-\left(4z-1\right)^2\)
Xac dinh gia tri nho nhat cua bieu thuc: T=x^2+2xy+2y^2-2x-2y-2
tinh gia tri cua cac bieu thuc sau:
a,x(x-6)-y(6-x) tai x=2006,y=2002
b,5x(x-y)-y(x-y) tai x=60,y=5
cho bieu thuc A=[x+2/x^2-x+x-2/x^2+x].x^2-1/x^2+2
a) tim dieu kien cua x de gia tri cua bieu thuc A duoc xac dinh
b) tinh gia tri cua bieu thuc A voi x = -200
bai 1
a = (3x / 2x + 4 ) + (x +3 /x ^ 2 - 4 )
a . tim x de gia tri phan thuc a duoc xac dinh
b. rut gon a
c. tinh gia trin cua a khi x bang -3
d . tim gia tri cua x de phan thuc co gia tri bang 2
tim tat ca cac so tu nhien x y thoa man x^2=y^2(x+y^4+2y^2)
tim tat ca cac so tu nhien x,y thoa man x^2=y^2(x+y^4+2y^2)