\(\left(x-4\right)^2< 2x\left(x-4\right)+16\\ \Leftrightarrow x^2-4x+4< 2x^2-8x+16\\ \Leftrightarrow2x^2-8x+16-x^2+4x-4>0\\ \Leftrightarrow x^2-4x+12>0\\ \Leftrightarrow\left(x^2-4x+4\right)+8>0\\ \Leftrightarrow\left(x-2\right)^2+8>0\)
Mà: `(x-2)^2>=0` với mọi x
`=>(x-2)^2+8>=8>0` với mọi x
=> x ∈ R
1) √(2x-1) <= 8-2x
2) √[(x+1)(4-x)] > x-2
3) √(x-2x^2+1) > 1-x
4) √(x+5) - √(x+4) > √(x+3)
5) √(5x-1) - √(x-1) > √(2x-4)
6) √(x+3) >= √(2x-8) + √(7-x)
7) √(x+2) - √(3-x) < √(5-2x)
8) √(x+1) > 3 - √(x+4)
9) √(5x-1) - √(4x-1)<= 3√x
10) { {√[2(x^2-16)]} / √(x-3) }+ √(x-3) > (7-x) / √(x-3)
Giúp mình 10 câu này với ạaa
i) \(2\sqrt{x+2+2\sqrt{x+1}}-\sqrt{x+1}=4\)
ii)\(\sqrt{x+4}+\sqrt{x-4}=2x-12+2\sqrt{x^2-16}\)
căn(x+4)+căn(x-4)=2x-12+2căn(x^2-16)
C = \(\sqrt{9x^2}-2x\left(x< 0\right)\)
D = x-4+\(\sqrt{16-8x+x^2}\)(x>4)
4) |3 - 2x| = x + 2
5) |2x - 1| = 5 - x
6) |- 3x| = x - 2
7) |2 - 3x| = 2x + 1
8) |2x - 1| + |4x ^ 2 - 1| = 0
9) (2x + 5)/(x + 3) + 1 = 4/(x ^ 2 + 2x - 3) - (3x - 1)/(1 - x)
10) (x - 1)/(x + 3) - x/(x - 3) = (7x - 3)/(9 - x ^ 2)
11) 5 + 96/(x ^ 2 - 16) = (2x - 1)/(x + 4) + (3x - 1)/(x - 4)
12) (2x)/(2x - 1) + x/(2x + 1) = 1 + 4/((2x - 1)(2x + 1))
13) (x + 2)/(x - 2) - 1/x = 2/(x ^ 2 - 2x)
14) x/(2x - 6) + x/(2x + 2) = (2x + 4)/(x ^ 2 - 2x - 3)
\(\sqrt{x^2-5x-6}=x-2\)
\(\sqrt{x^2-8x+16}=4-x\)
\(\sqrt{x^2-2x}=2-x\)
\(\sqrt{2x+27}-6=x\)
6) \(\sqrt{x^2+12x+36}=-x-6\)
7) \(\sqrt{9x^2-12x+4}=3x-2\)
8) \(\sqrt{16-24x+9x^2}=2x-10\)
9) \(\sqrt{x^2-6x+9}==2x-3\)
10) \(\sqrt{x^2-3x+\dfrac{9}{4}}=\dfrac{3}{x}x-4\)
A. \(\sqrt{9x^2+16}=2\sqrt{2x+4}+4\sqrt{x-2}\)
B. \(2\sqrt{x^2-\frac{1}{4}+\sqrt{x^2+x+\frac{1}{4}}}=2x^3+x^2+2x+1\)
Giải phương trình:
\(\sqrt{x-4}+\sqrt{x+4}=2\sqrt{x^2-16}+2x-12\)
C =
D = x-4+(x>4)
