Rút gọn:
B= 8/√x -2 - √x +26/x-4
Rút gọn:B=16-(x+1)^2/x^2+10x+25
Bài làm
\(B=\frac{16-\left(x+1\right)^2}{x^2+10x+25}\)
\(B=\frac{\left(4-x-1\right)\left(4+x+1\right)}{\left(x+5\right)^2}\)
\(B=\frac{\left(3-x\right)\left(x+5\right)}{\left(x+5\right)^2}\)
\(B=\frac{3-x}{x+5}\)
# Học tốt #
Rút gọn:B=(1-1/2).(1-1/3).(1-1/4).....(1-1/20)
1-1/2=1/2
1-1/3=2/3
......1-1/20= 19/20
B =1/2.2/3.3/4.4/5.....19/20
rut gon ta co B 1/20
nho k cho em nha
1, Rút gọn
a, 8^26+4^20/4^25+64^5
b, 2^2017-(2^2016+2^2015+2^2014+...+2+1)
c, Tìm x : x^10=25:x^8
d, cho hình vẽ:
Rút gọn :\(\dfrac{x^{24}+x^{20}+x^{16}+...+x^4+1}{x^{26}+x^{24}+x^{22}+...+x^2+1}\)
Ta có: \(\dfrac{x^{24}+x^{20}+x^{16}+...+x^4+1}{x^{26}+x^{24}+x^{22}+...+x^2+1}\)
\(=\dfrac{x^{24}+x^{20}+x^{16}+...+x^4+1}{\left(x^{26}+x^{22}+...+x^2\right)+\left(x^{24}+x^{20}+x^{16}+...+x^4+1\right)}\)
\(=\dfrac{x^{24}+x^{20}+x^{16}+...+x^4+1}{x^2\left(x^{24}+x^{20}+...+1\right)+\left(x^{24}+x^{20}+x^{16}+...+x^4+1\right)}\)
\(=\dfrac{x^{24}+x^{20}+x^{16}+...+x^4+1}{\left(x^{24}+x^{20}+x^{16}+...+1\right)\left(x^2+1\right)}\)
\(=\dfrac{1}{x^2+1}\)
=x24+x20+x16+...+x4+1(x26+x22+...+x2)+(x24+x20+x16+...+x4+1)=x24+x20+x16+...+x4+1(x26+x22+...+x2)+(x24+x20+x16+...+x4+1)
=x24+x20+x16+...+x4+1(x24+x20+x16+...+1)(x2+1)
Rút gọn:B=2^100-2^99+2^98-2^97+....+2^2
Đây nha. Bài này dễ mà chỉ cần nhân lên đúng với số của cơ số là được
2B= 2^101-2^100-2^99+...+2^3
2B-B= (2^101-2^100-2^99+...+2^3)-(2^100-2^99+....+2^2)
B= 2^101-2^2
RÚT GỌN\(\frac{x^{24}+x^{20}+.......+x^4+1}{x^{26}+x^{24}+......+x^2+1}\)
\(\frac{x^{24}+x^{20}+...+x^4+1}{x^{26}+x^{24}+...+x^2+1}=\frac{x^{24}+x^{20}+...+x^4+1}{\left(x^{24}+x^{20}+...+x^4+1\right)+\left(x^{26}+x^{22}+...+x^2\right)}\)
\(=1-\frac{x^2\left(x^{24}+x^{20}+...+x^4+x^1\right)}{\left(1+x^2\right)\left(x^{24}+2^{20}+...+x^4+1\right)}=1-\frac{x^2}{1+x^2}\)
\(=\frac{1+x^2-x^2}{1+x^2}=\frac{1}{1+x^2}\)
Hoặc cách khác:
\(\frac{x^{24}+x^{20}+...+x^4+1}{x^{26}+x^{24}+...+x^2+1}=\frac{x^{24}+x^{20}+...+x^4+1}{\left(x^{24}+x^{20}+...+x^4+1\right)+x^2\left(x^4+x^{20}+...+x^4+1\right)}\)
\(=\frac{x^{24}+x^{20}+...+x^4+1}{\left(x^2+1\right)\left(x^{24}+x^{20}+...+x^4+1\right)}=\frac{1}{x^2+1}\)
Ở cách thứ 2,mình viết nhầm tí: \(x^2\left(x^4+x^{20}+...+x^4+1\right)\rightarrow x^2\left(x^{24}+x^{20}+...+x^4+1\right)\) giúp mình nha,Đánh thiếu số 2 : một lỗi sai chết người=)
Bài 19 Rút gọn
1) (x+2)^2+(3-x)^2
2) (4-x)^2 -(x-3)^2
3) (x-5)(x+5)-(x+5)^2
4) (x-3)^2-(x-4)(x+4)
5) (y^2 -6y+9)-(3-y)^2
6. (2x+3)² –(2x–3).(2x+3)
1) Ta có: \(\left(x+2\right)^2+\left(x-3\right)^2\)
\(=x^2+4x+4+x^2-6x+9\)
\(=2x^2-2x+13\)
2) Ta có: \(\left(4-x\right)^2-\left(x-3\right)^2\)
\(=\left(4-x-x+3\right)\left(4-x+x-3\right)\)
\(=-2x+7\)
3) Ta có: \(\left(x-5\right)\left(x+5\right)-\left(x+5\right)^2\)
\(=x^2-25-x^2-10x-25\)
=-10x-50
4) Ta có: \(\left(x-3\right)^2-\left(x-4\right)\left(x+4\right)\)
\(=x^2-6x+9-x^2+16\)
=-6x+25
5) Ta có: \(\left(y^2-6y+9\right)-\left(y-3\right)^2\)
\(=y^2-6y+9-y^2+6y-9\)
=0
6) Ta có: \(\left(2x+3\right)^2-\left(2x-3\right)\left(2x+3\right)\)
\(=4x^2+12x+9-4x^2+9\)
=12x+18
Bài 19 rút gọn
1) (x+2)^2+(3-x)^2
2) (4-x)^2-(x-3)^2
3) (x-5)(x+5)-(x+5)^2
4)(x-3)^2-(x-4)(x+4)
5) (y^2-6y+9)-(3-y)^2
6) (2x+3)^2-(2x-3)(2x+3)
1) Ta có: \(\left(x+2\right)^2+\left(x-3\right)^2\)
\(=x^2+4x+4+x^2-6x+9\)
\(=2x^2-2x+13\)
2) Ta có: \(\left(4-x\right)^2-\left(x-3\right)^2\)
\(=\left(4-x-x+3\right)\left(4-x+x-3\right)\)
\(=\left(-2x+7\right)\cdot1\)
\(=-2x+7\)
3) Ta có: \(\left(x-5\right)\left(x+5\right)-\left(x+5\right)^2\)
\(=x^2-25-x^2-10x-25\)
\(=-10x-50\)
rút gọn B=\(\frac{x^{28}+x^{24}+x^{20}+...+x^4+1}{x^{30}+x^{28}+x^{26}+...+x^2+1}\)