rút gọn biểu thức sau
\(\left(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}\right):\left(1-\frac{3\sqrt{x}}{\sqrt{x}+1}\right)\)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Xét \(\Delta BDC\)và \(\Delta EBC\)
ta có \(\widehat{BDC}=\widehat{EBC}\)(cùng phụ với \(\widehat{BED}\))
\(\widehat{DCB}=\widehat{BCE}=90^0\)
nên \(\Delta BDC\)đông dạng \(\Delta EBC\)(g-g)
dễ chứng minh \(\Delta BCD\approx\Delta EBD\left(g-g\right)\)
nên \(\frac{BD}{DE}=\frac{CD}{BD}\Rightarrow BD^2=CD\cdot DE\)
Áp dụng định lí Pi-ta-go cho \(\Delta ABC\)vuông tại A, ta có:
\(AB^2+AC^2=BC^2\)
\(\Leftrightarrow BC^2=8^2+15^2\)
\(\Leftrightarrow BC=\sqrt{289}=17\)
Tỉ số lượng giác của góc B là:
\(\sin B=\frac{AC}{BC}=\frac{15}{17}\)
\(\cos B=\frac{AB}{BC}=\frac{8}{17}\)
\(\tan B=\frac{AC}{AB}=\frac{15}{8}\)
\(\cot B=\frac{AB}{AC}=\frac{8}{15}\)
Tỉ số lượng giác của góc C là:
\(\sin C=\cos B=\frac{8}{17}\)
\(\cos C=\sin B=\frac{15}{17}\)
\(\tan C=\cot B=\frac{8}{15}\)
\(\cot C=\tan B=\frac{15}{8}\)
Chúc bn hok tốt
bn nhớ tk cho minh nha
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}\)
\(=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}\)
\(=\frac{2}{2\text{x}3}+\frac{2}{3\text{x}4}+\frac{2}{4\text{x}5}+\frac{2}{5\text{x}6}+\frac{2}{6\text{x}7}+\frac{2}{7\text{x}8}\)
\(=2\text{x}\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\right)\)
\(=2\text{x}\left(\frac{1}{2}-\frac{1}{8}\right)\)
\(=2\text{x}\frac{3}{8}=\frac{3}{4}\)
\(x^7+y^7=\left(x^3+y^3\right)\left(x^4+y^4\right)-x^3y^4-x^4y^3\)
Biểu diễn các số hạng theo a, b
\(x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)=a^3-3ab\)
\(x^4+y^4=\left(x^2+y^2\right)^2-2x^2y^2=\left(a^2-2b\right)^2-2b^2\)
Khi đó:\(x^7+y^7=\left(a^3-3ab\right)\left[\left(a^2-2b\right)^2-2b^2\right]-ab^3\)
A = 1002 - 992 + 982 - 972 + ...... + 22 - 12
= ( 100 - 99 ) ( 100 + 99 ) + ( 98 - 97 ) ( 98 + 97 ) + ......... + ( 2 - 1 ) ( 2 + 1 )
= 1 + 2 + 3 + ......... + 99 + 100
= ( 100 + 1 ) . 100 : 2 = 5050
B = 3 ( 22 + 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 12
= ( 22 - 1 ) ( 22 + 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 1
= ( 24 - 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 1
= ( 28 - 1 ) ( 28 + 1 ) ... ( 264 + 1 ) + 1
= ( 216 - 1 ) ( 216 + 1 ) ... ( 264 + 1 ) + 1
= ( 232 - 1 ) ( 232 + 1 ) ( 264 + 1 ) + 1
= ( 264 - 1 ) ( 264 + 1 ) + 1
= 2128 - 1 + 1
= 2128
C = ( a + b + c )2 + ( a + b - c )2 - 2 ( a + b )2
= a2 + b2 + c2 + 2ab + 2bc + 2ca + a2 + ab - ac + ab + b2 - bc - ac - bc + c2 - 2 ( a2 + 2ab + b2 )
= a2 + b2 + c2 + 2ab + 2bc + 2ca + a2 + ab - ac + ab + b2 - bc - ac - bc + c2 - 2a2 - 4ab - 2b2
= 2c2
Bài làm:
a) \(A=100^2-99^2+98^2-97^2+...+2^2-1^2\)
\(A=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\)
\(A=100+99+98+97+...+2+1\)
\(A=\frac{\left(100+1\right)\times100}{2}=5050\)
b) \(B=3\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1^2\)
\(B=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)
\(B=\left(2^4-1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)
...
\(B=\left(2^{64}-1\right)\left(2^{64}+1\right)+1\)
\(B=2^{128}-1+1=2^{128}\)
c) \(C=\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a+b\right)^2\)
\(C=a^2+b^2+c^2+2\left(ab+bc+ca\right)+a^2+b^2+c^2+2\left(ab-bc-ca\right)-2a^2-4ab-2b^2\)
\(=2c^2+2\left(ab+bc+ca+ab-bc-ca-2ab\right)\)
\(=2c^2+2.0=2c^2\)
a, \(6^2:4.3+2.5^2=36:4.3+2.25\)'
\(=9.3+50=27+50=77\)
b, \(2\left(5.4^2-18\right)=2\left(5.16-18\right)\)
\(=2.5.16-2.18=10.16-36\)
\(=160-36=124\)
c, \(5.4^2-18:3^2=5.4.4-18:3^2\)
\(=20.4-18:9=80-2=78\)
\(a,6^2:4.3+2.5^2\)
\(=9.3+2.25\)
\(=27+50\)
\(=77\)
\(b,2.\left(5.4^2-18\right)\)
\(=2.\left(80-18\right)\)
\(=2.62\)
\(=124\)
\(c,5.4^2-18:3^2\)
\(=5.16-18:9\)
\(=80-2\)
\(=78\)
\(d,3^3.18-3^3.12\)
\(=3^3.6.3-3^3.6.2\)
\(=3^3.6.\left(3-2\right)\)
\(=27.6.1\)
\(=162\)
\(e,39.213+84.39\)
\(=39.\left(213+84\right)\)
\(=39.297\)
\(=11583\)
\(j,80-\left[130-\left(12-4\right)^2\right]\)
\(=80-\left[130-8^2\right]\)
\(=80-66\)
\(=14\)
Học tốt