gia tri nho nhat cua A=trị đối x2+5 tất cả mũ 2+(-5x2-1)4
Gia tri nho nhat cua A = |x^2 + 5|^2+ (-5x^2 - 1)^4 la
tim gia tri nho nhat cua bieu thuc tim gia tri nho nhat cua bieu thuc x^4-4x^3+12x^2-16x+16
1.gia tri nho nhat cua x^2-x+1
2. gia tri nho nhat cua x^2+10x+2041
Bài 1:
\(x^2-x+1=x^2-x+\frac{1}{4}+\frac{3}{4}\)
\(=\left(x^2-x+\frac{1}{4}\right)+\frac{3}{4}\)
\(=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)
Dấu "=" khi \(x=\frac{1}{2}\)
Vậy \(Min=\frac{3}{4}\) khi \(x=\frac{1}{2}\)
Bài 2:
\(x^2+10x+2041=x^2+10x+25+2016\)
\(=\left(x^2+10x+25\right)+2016\)
\(=\left(x+5\right)^2+2016\ge2016\)
Dấu "=" khi \(x=-5\)
Vậy \(Min=2016\) khi \(x=-5\)
Tim gia tri nho nhat cua P={x^2+1}^2+{y^4+5}^2
tim gia tri nho nhat cua (x+1)(x+2)(x+4)(x+5)
gia tri nho nhat cua a=(x-3)^2+/y+5/^3-4 la
Vì \(\left(x-3\right)^2\ge0\forall x\) \(;\left|y+5\right|\ge0\forall y\)
\(\Rightarrow\left(x-3\right)^2+\left|y+5\right|\ge0\)
\(\Rightarrow A=\left(x-3\right)^2+\left|y+5\right|-4\ge-4\)
Dấu "=" xảy ra <=> \(\orbr{\begin{cases}\left(x-3\right)^2=0\\\left|y+4\right|=0\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\y=-4\end{cases}}}\)
Vậy GTNN của A là - 4 tại x = 3; y = - 4
1.gia tri lon nhat cua bieu thuc 7x-2x2
2.gia tri x>1 thoa man (9x-7)2=(5-2x)2
3.gia tri nho nhat cua x4+x2-5.42
1.ta có: 7x-2x^2=-2(x^2-7/2x)
=-2(x^2-2*7/4x+49/16-49/16)
=-2(x-7/4)^2+49/8 <=49/8
Dấu bằng xáy ra <=> x=7/4
Vậy max=49/8 <=> x=7/4
tim gia tri nho nhat cua cac da thuc
Q=2 x mũ 2 - 6x
M = x mũ 2 +y mũ 2-x+6y+10
\(Q=2x^2-6x\)
\(Q=2.(x^2 - 2.\dfrac{3}{2}.x+\dfrac{9}{4}\text{)}-\dfrac{9}{2} \)
\(Q=2.(x-\dfrac{3}{2})^2-\dfrac{9}{2}\ge\dfrac{-9}{2}\)
\(\Rightarrow Min_A=\dfrac{-9}{2}\) khi \(x=\dfrac{3}{2}\) .
\(M=x^2+y^2-x+6y+10\)
\(M=\left(x^2-x+\dfrac{1}{4}\right)+\left(y^2+6y+9\right)+\dfrac{3}{4}\)
\(M=\left(x-\dfrac{1}{2}\right)^2+\left(y+3\right)^2+\dfrac{3}{4}\)
\(M=\left(x-\dfrac{1}{2}\right)^2+\left(y+3\right)^2\ge0\)
\(\Rightarrow\left(x-\dfrac{1}{2}\right)^2+\left(y+3\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)
\(\Rightarrow Min_M=\dfrac{3}{4}\) khi \(x=\dfrac{1}{2},y=-3.\)
gia tri cua x de a=(-3-x)^2+5 dat gia tri nho nhat
Ta có: (-3-x)2\(\ge\)0 với mọi x
=>(-3-x)2+5 \(\ge\)0+5 với mọi x
=>A\(\ge\)5 với mọi x
Vậy A Min = 5 khi x=-3