\(\sqrt{6+2\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
= \(\sqrt{5+2\sqrt{5}+1}-\sqrt{5+4\sqrt{5}+4}\)
= \(\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{\left(\sqrt{5}+2\right)^2}\)
= \(\sqrt{5}+1-\sqrt{5}-2\)
= \(-1\)
Giải các phương trình vô tỉ (Phương trình có chứa căn thức)
1) \(\sqrt{x^2-20x+100}=10\)
2) \(\sqrt{x+2\sqrt{x}+1}=6\)
3) \(\sqrt{x^2-6x+9}=\sqrt{4+2\sqrt{3}}\)
4) \(\sqrt{3x+2\sqrt{3x}+1}=5\)
5) \(\sqrt{x^2+2x\sqrt{3}+3}=\sqrt{4-2\sqrt{3}}\)
6) \(\sqrt{6x+4\sqrt{6x}+4}=7\)
7) \(\sqrt{2x^2-2x\sqrt{6}+3}-\sqrt{5-\sqrt{24}}=0\)
8) \(\sqrt{3-2\sqrt{2}}-\sqrt{x^2-2x\sqrt{2}+2}=0\)
9) \(\sqrt{11-\sqrt{120}}=\sqrt{5x^2+x\sqrt{120}+6}\)
Giải PT:
a) \(\dfrac{9x-7}{\sqrt{7x+5}}=\sqrt{7x+5}.\)
b) \(\sqrt{4x-20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4.\)
c) \(2x-x^2+\sqrt{6x^2-12x+7}=0.\)
d) \(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6.\)
Phân tích đa thức thành nhân tử
1. \(x\sqrt{x}+\sqrt{x}-x-1\)
2. \(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
3. \(x-\sqrt{x}-2\)
4. \(x-3\sqrt{x}+2\)
5. \(-6x+5\sqrt{x}+1\)
6. \(x+4\sqrt{x}+3\)
7. \(3\sqrt{a}-2a-1\)
8. \(x+2\sqrt{x-1}\)
9. \(7\sqrt{x}-6x-2\)
10. \(x-5\sqrt{x}+6\)
11. \(x-2+\sqrt{x^2-4}\)
giải các phương trình sau:
\(\)1, \(\sqrt{10-x}+\sqrt{x+3}\)=5
2, \(\sqrt{15-x}+\sqrt{3-x}\)=6
3, \(\sqrt{4x+1}-\sqrt{3x+4}=1\)
4, \(\sqrt{x+\sqrt{2x-1}}\)+\(\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
5, \(\sqrt{x^2-4x+4}+\sqrt{x^2-6x+9}=1\)
Bài 1: Giải PT
a) \(\sqrt{x^2-1}-x^2+1=0\)
b) \(\sqrt{x^2-4}-x+2=0\)
c) \(\sqrt{x^4-8x^2+16}=2-x\)
d) \(\sqrt{9x^2+6x+1}\sqrt{11-6\sqrt{2}}\)
e) \(\sqrt{4^2-9}=2\sqrt{2x+3}\)
f) \(\sqrt{4x-20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
Giải phương trình:
a. \(\sqrt{x^2-6x+9}=2\)
b. \(\sqrt{1-x}=\sqrt{6-x}-\sqrt{-5-2x}\)
c. \(\sqrt{x^2-4}-\sqrt{x-2}=0\)
Tính:
a,\(\sqrt{6-2\sqrt{5}}-\sqrt{20}-1\)
b,\(\sqrt{9}+4\sqrt{5}-\sqrt{9-4\sqrt{5}}\)
c,(\(\sqrt{4-2\sqrt{3}}-1).\frac{1}{2\sqrt{3}-4}\)
(cảm ơn)
Giả phương trình:
a/ \(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
b/ \(\sqrt{2-x^2+2x}+\sqrt{-x^2-6x-8}=1+\sqrt{3}\)
\(\sqrt{5-2\sqrt{2+\sqrt{9+4\sqrt{2}}}}\sqrt{\sqrt{3-\sqrt{4-\sqrt{2-\sqrt{6-4\sqrt{10-4\sqrt{6}}}}}}}\)
