1, tính a/ (3+√5)(√10 - √2)√(3-√5)
b/[√2-√(3-√5)].√2
c/(√10 + √6).√(8-2√15)
2, tìm x biết a/ √(x+5)=1+√x
b/√x + √(x-1)=1
c/ √(3-x) + √(x-5)=10
3, phân tích đa thức thành nhân tử:
a/ ab+b√a+√a+1 với a ≥0
b/ x-2√xy + y với x,y ≥ 0
c/√xy + 2√x - 3√y -6 với x,y ≥ 0
4, chứng minh rằng a/ (4+√15).(√10-√6).√(4-√15)=2
b/ √a + √b > √(a+b) (a,b>0)
5, Cho √(8-a) + √(5+a) = 5 tính √[(8-a).(5+a)]
6, rút gọn √(7+2√10)-√15
P/s : mn giúp e với nha
a)\(\left(\sqrt{3}-\sqrt{2}+1\right).\left(\sqrt{3}-1\right).\)
b)\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
c)\(2\sqrt{8\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}\)
d)\(\left(\sqrt{8}-5\sqrt{2}+\sqrt{20}\right).\sqrt{5}-\left(3.\sqrt{\frac{1}{10}}+10\right)\)
giúp mk zới:((
a) \(A=\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
b) \(B=\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}+\frac{12}{3-\sqrt{6}}\right)\left(\sqrt{6}+11\right)\)
Giúp mình với dang cần gấp
1) |2x - 1| = 5
2) |2x - 1| = |x + 5|
3) |3x + 1| = x - 2
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)
a/ (√10+√2) (6-2√5)√(3+√5)
b/ √(13-√160) - √(53-4√90)
c/ √(10+√24+√40+√60)
d/ (√2+√3+√6+√8+√16)/(√2+√3+√4)
e/ [√216/3-(2√3-√6)/(√8-2)] ×1/√6
f/ 1/(√2-√3) × √[(3√2-2√3)/(3√2+2√3)]
g/ 1/(√1+√2) + 1/(√2+√3) + ......+ 1/(√2017+√2018)
Thực hiện phép tính:
a)\(\frac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\)
b) \(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
c) \(\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}\)
d)\(\frac{\left(\sqrt{5}+2\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
Giúp vs, làm câu nào cx đc, làm hết thì tốt
a) \(\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)
b) \(\sqrt{27-10\sqrt{2}}+\sqrt{18-8\sqrt{2}}\)
c) \(\sqrt{3-\sqrt{5}}.\sqrt{8}\)
d) \(\dfrac{\sqrt{2-\sqrt{3}}}{\sqrt{2}}.\sqrt{8}\)
e) \(\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\dfrac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
g) \(\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2-\sqrt{2}}{\sqrt{2}-1}-\left(\sqrt{2}+3\right)\)
h) \(\dfrac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54}.\sqrt[3]{4}\)
i) \(\left(\sqrt[3]{25}-\sqrt[3]{10}+\sqrt[3]{4}\right).\left(\sqrt[3]{5}+\sqrt[3]{2}\right)\)
k) \(\sqrt[3]{\left(4-2\sqrt{3}\right)\left(\sqrt{3}-1\right)}\)
L) \(A=\sqrt[3]{10+14\sqrt{2}}+\sqrt[3]{10-14\sqrt{2}}\)
tìm tích
a/ (1/2 +1) . (1/3 +1) . (1/4 +1) ....(1/999 +1)
b/ (1/2 -1) . (1/3 -1). (1/4 -1)....(1/1000 -1)
c/ 3/2^2 .8/3^2 .15/4^2 ...99/10^2
giúp mình với nha ,mình cần gấp đó .Thanks
Rút gọn các biểu thức sau:
a ) ( 8 − 3 2 + 10 ) 2 − 5 b ) 0 , 2 ( − 10 ) 2 ⋅ 3 + 2 ( 3 − 5 ) 2 c ) 1 2 1 2 − 3 2 ⋅ 2 + 4 5 ⋅ 200 : 1 8 d ) 2 ( 2 − 3 ) 2 + 2 ⋅ ( − 3 ) 2 − 5 ( − 1 ) 4