1.gia tri nho nhat cua bieu thuc A=\(\frac{x^2}{4}+3x+y^2-\frac{14}{5}y+\frac{425}{25}\)la
2.cho x, y nguyen thoa man x2+4x+y2-12=0 . khi do gia tri lon nhat P=x2+y2 la Pmax=?
1. cho phan tuc A=\(\frac{x^2+5x+4}{x^2+x-12}\)tap hop cac gia tri cua x de phan thuc A ko xac dinh la
2.cho hinh thang ABCD co dien tich la18cm2. duong cao AH =3cm . Do dai duong trung binh hinh thang la
3.cho x, y nguyen thoa man x2+4x+y2-12=0 . khi do gia tri lon nhat P=x2+y2 la Pmax=?
4.gia tri nho nhat cua bieu thuc A= \(\frac{x^2}{4}+3x+y^2-\frac{14}{5}y+\frac{425}{25}la\)
1.để Ak xđịnh thì x2+x-12=0
<=>x2+4x-3x-12=0
<=>x(x+4)-3(x+4)=0
<=>(x+4)(x-3)=0 <=> x=-4 hoặc x=3
Vậy để A k xđịnh <=> x=-4 hoặc x=3
**** cho mìk vs nha bạn
cho x,y la cac so duong thay doi va thoa man dieu kien x+y\(\le\)1. tim gia tri nho nhat cua bieu thuc M=\(\frac{1}{x^2+y^2}+\frac{1}{xy}+4xy\)
Ta có: \(\frac{1}{x^2+y^2}+\frac{1}{xy}+4xy\)
\(=\left(\frac{1}{x^2+y^2}+\frac{1}{2xy}\right)+\left(4xy+\frac{1}{4xy}\right)+\frac{1}{4xy}\)
\(\ge\frac{4}{\left(x+y\right)^2}+2\sqrt{4xy.\frac{1}{4xy}}+\frac{1}{\left(x+y\right)^2}\)\(\ge4+2+1=7\)
Dấu = xảy ra khi \(x=y=\frac{1}{2}\)
Vậy \(\left(\frac{1}{x^2+y^2}+\frac{1}{xy}+4xy\right)_{Min}=7\Leftrightarrow x=y=\frac{1}{2}\)
à nhầm, bạn pham trung thanh làm đúng rồi đấy mọi người ủng hộ bạn ấy nha
1. so x>0 thoa man \(\frac{5}{x}=\frac{x+1}{22}\)
2. GTLN cua x thoa man \(5^{\left(x-2\right)\left(x+3\right)}\)
3. Gia tri x<0 thoa man /\(x^2+50\)/=/\(-2x^2\)-1/
4. Gia tri nguyen cua x thoa man \(\left(3x-4\right)^5\)=\(^{\left(3x-4\right)^7}\)la x=
5. So gia tri cua x thoa man /x-2014/+/x-2015/=0
6. Gia tri cua x de bieu thuc A=\(\frac{x-3+5}{3-x+2}\)dat gia tri lon nhat la x=
cho hai so duong xy thoa man \(\frac{4}{x^2}+\frac{5}{y^2}\ge9\) tim gia tri nho nhat cua bieu thuc\(Q=2x^2+\frac{6}{x^2}+3y^2+\frac{8}{y^2}\)
\(Q=2x^2+\frac{2}{x^2}+3y^2+\frac{3}{y^2}+\frac{4}{x^2}+\frac{5}{y^2}\)
Áp dụng cô si ,ta có
\(2x^2+\frac{2}{x^2}\ge2\sqrt{2x^2\cdot\frac{2}{x^2}}=4\)
\(3y^2+\frac{3}{y^2}\ge2\sqrt{3y^2\cdot\frac{3}{y^2}}=6\)
\(\Rightarrow Q\ge4+6+9=19\)
Dấu "=" xảy ra khi x=y=1
1. nghiem nho nhat cua da thuc 11x-2x2-15
2.gia tri x nho nhat thoa man : 4x2+7x+3=0
3.gia tri lon nhat cua bieu thuc7x-2x2
.
cho x,y,z la cac so huu ti duong thoa man x+1/yz y +1/xz z+1/xy la cac so nguyen tim gia tri lon nhat cua bieu thuc A=x+y^2+z^3
1. tich cac gia tri x thoa man x2-\(\frac{1}{10}\)x-\(\frac{1}{5}\)+0
2.gia tri cua x de bieu thuc A=6x2+7x-8 dat gia tri nho nhat
3.tích cac gia tri cua x thoa man (2x-1)2=(2-x)2
TIM GIA TRI LON NHAT CUA BIEU THUC :
C=2+12/3x/X+5/+4
TIM GIA TRI NHO NHAT CUA BIEU THUC
C= -15/ 4x / 3X+7/+3
Tim gia tri lon nhat va gia tri nho nhat cua bieu thuc sau: A=\(\frac{x+1}{x^2+x+1}\)
GTLN :
\(A=\frac{x+1}{x^2+x+1}=\frac{\left(x^2+x+1\right)-x^2}{x^2+x+1}=1-\frac{x^2}{x^2+x+1}\)
Vì \(\frac{x^2}{x^2+x+1}=\frac{x^2}{\left(x+\frac{1}{2}\right)^2+\frac{3}{4}}\ge0\forall x\) nên \(A=1-\frac{x^2}{x^2+x+1}\le1\forall x\) có GTLN là 1
GTNN :
\(A=\frac{x+1}{x^2+x+1}=\frac{-\frac{1}{3}x^2-\frac{1}{3}x-\frac{1}{3}+\frac{1}{3}x^2+\frac{4}{3}x+\frac{4}{3}}{x^2+x+1}=\frac{-\frac{1}{3}\left(x^2+x+1\right)+\frac{1}{3}\left(x+2\right)^2}{x^2+x+1}\)
\(=-\frac{1}{3}+\frac{\frac{1}{3}\left(x+2\right)^2}{x^2+x+1}=-\frac{1}{3}+\frac{\left(x+2\right)^2}{3\left(x^2+x+1\right)}\ge-\frac{1}{3}\) có GTNN là \(-\frac{1}{3}\)