Giải các pt sau:
1, \(\sqrt{x^2+x+1}=2x+\sqrt{x^2-x+1}\)
2, \(2x^2+2x+6=2x\sqrt{x^2-x+1}+4\sqrt{3x+1}\)
3, \(\left(\sqrt{x+3}-\sqrt{x}\right)\left(1+\sqrt{x^2+3x}\right)=3\)
4, \(\sqrt{2x^2-1}+\sqrt{x^2-3x-2}=\sqrt{2x^2-2x+3}+\sqrt{x^2-x+2}\)
5, \(13\sqrt{x-1}+9\sqrt{x+1}=16x\)
2)
a) gpt \(x^3+5x^2+10x=\left(3x^2+3x+6\right)\sqrt{x+2}\)
b)tìm nghiệm nguyên dương :\(x^2-y^2+x^2y-xy=x+14\)
Giải pt \(x\left(3-\sqrt{3x-1}\right)=\sqrt{3x^2+2x-1}-x\sqrt{x+1}+1\)
1)
a) gpt \(\sqrt{5-3x}+\sqrt{x+1}=\sqrt{3x^2-4x+4}\)
b) ghpt \(\left\{{}\begin{matrix}2xy+4x+3y+6=0\\4x^2+y^2+12x+4y+9=0\end{matrix}\right.\)
1) gpt \(x^2+3x\sqrt{\dfrac{x^2+1}{x}}=10x-1\)
2) ghpt \(\left\{{}\begin{matrix}x^2+y^2+2\left(x+y\right)=6\\xy\left(x+2\right)\left(y+2\right)=9\end{matrix}\right.\)
3) cho a,b,c dương thỏa abc=1
CMR \(\dfrac{2}{a^2\left(b+c\right)}+\dfrac{2}{b^2\left(c+a\right)}+\dfrac{2}{c^2\left(a+b\right)}\ge3\)
Giải phương trình
a, \(\sqrt{x^2-x+9}=2x+1\)
b. \(\sqrt{5x+7}-\sqrt{x+3}=\sqrt{3x+1}\)
c. \(x^2-3x-10+3\sqrt{x.\left(x-3\right)}=0\)
d. \(\sqrt{2-x}+\sqrt{4-x}=x^2-6x+11\)
e. \(x+6\sqrt{x+8}+4\sqrt{6-2x}=27\)
giải pt sau:
1, \(\dfrac{x}{x+3}\)+\(\dfrac{2}{x-1}\)=\(\dfrac{12}{x^2+2x-3}\)
2, \(\sqrt{x^2+3x+12}\)= x2 +3x
3, \(\sqrt{5x^2}-6x-4\)= 2(x-1)
4, x2 +6 = 4 \(\sqrt{x^3-2x^2+3}\)
5, \(\sqrt{\left(2x+1\right)\left(x^2+3\right)}\)= 2x2 -2x -7
mọi người giúp mk nha cảm ơn mn nhiều <3
Rút gọn
a,\(E=\sqrt{\left(3x+1\right)^2}+3\sqrt{\left(1-x\right)^2}\) với x<1
b,\(F=\sqrt{\left(2x+4\right)^2}+2\sqrt{\left(3-x\right)^2}\)
Cho \(x=\dfrac{\sqrt{28-16\sqrt{3}}}{\sqrt{3}-1}\). Tính \(B=\left(x^6+3x^5-2x^3+x^2-1\right)^{2018}\)
