a) \(A=\sqrt{x^2+2x+5}=\sqrt{\left(x+1\right)^2+4}\ge\sqrt{4}=2\forall x\in R.\)
GTNN của A = 2 khi x = -1.
b) \(B=\sqrt{x^2+2x+5}+\sqrt{2x^2+4x+3}=\sqrt{\left(x+1\right)^2+4}+\sqrt{2\left(x+1\right)^2+1}\ge\sqrt{4}+1=3\)
GTNN của B = 3 khi x = -1.
1) \(\sqrt{x^2}=2x-5\)
2) \(\sqrt{25x^2-10x+1}=2x-6\)
3) \(\sqrt{25-10x+x^2}=2x-5\)
4) \(\sqrt{1-2x+x^2}=2x-1\)
5) \(\sqrt{4x^2+4x+1}=-x-3\)
Giải phương trình:
a) \(\sqrt{x^2+4}=\sqrt{2x+3}\)
b) \(\sqrt{x^2-6x+9}=2x-1\)
c) \(\sqrt{4x+12}=\sqrt{9x+17}-5\)
d) \(\sqrt{4x^2-6x+1}=\left|2x-5\right|\)
6. giải PT
a.\(\sqrt{2x+5}=\sqrt{1-x}\)
b.\(\sqrt{x^2-x}=\sqrt{3-x}\)
c.\(\sqrt{2x^2-3}=\sqrt{4x-3}\)
\(\sqrt{x+2\sqrt{x-1}}=2\)
\(\sqrt{4x^2-20x+25}+2x=5\)
\(\sqrt{2x^2-3}=\sqrt{4x-3}\)
\(\sqrt{x^2-x-6}=\sqrt{x-3}\)
\(\sqrt{x^2-x}=\sqrt{3-x}\)
tìm GTNN của biểu thức
\(\sqrt{x^2-2x+10}+\sqrt{x^2+4x+5}\)
tìm GTNN của biểu thức
\(\sqrt{x^2-2x+10}+\sqrt{x^2+4x+5}\)
Tìm GTLN,GTNN :
a) \(A=2x-6\sqrt{x}-1\)
b) \(C=\frac{1}{-2x+4\sqrt{x}+3}\)
c) \(E=\sqrt{4x^2-4x+1}+\sqrt{4x^2-12x+9}\)
d) \(F=\sqrt{2x-7}+\sqrt{5-2x}\)
e) \(A=-3x+6\sqrt{x}+3\)
h) \(E=\sqrt{2x+1}-\sqrt{2x-8}\)
i) \(F=\sqrt{3x-2}+\sqrt{5-3x}\)
mình cần gấp hôm nay ạ, giúp mình với ạ
a)\(\sqrt{X^2-3X+2}=3-X\)
b)\(\sqrt{4x^2-20x+25}+2x=5\)
c)\(\sqrt{\left(3-2x\right)^2}=4\)
1)\(7\sqrt{3x-7}+\left(4x-7\right)\sqrt{7-x}=32\)
2)\(4x^2-11x+6=\left(x-1\right)\sqrt{2x^2-6x+6}\)
3)\(9+3\sqrt{x\left(3-2x\right)}=7\sqrt{x}+5\sqrt{3-2x}\)
4)\(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
5)\(\frac{6-2x}{\sqrt{5-x}}+\frac{6+2x}{\sqrt{5+x}}=\frac{8}{3}\)
6)\(2\left(5x-3\right)\sqrt{x+1}+\left(x+1\right)\sqrt{3-x}=3\left(5x+1\right)\)
7)\(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-14x\)
