so sánh các số sau
a) A=163^2+74*163+37^2
B=147^2-94*147+47^2
b)C=(2^2+4^2+...+100^2)
và D=3^8*7^8-(21^4-1)(21^4+1|)
Tính hợp lí:
a) A= 1995^3+1/1995^2-1994
b) B= 3^8.7^8-(21^4-1).(21^4+1)
c) C= 163^2+74.163+37^2
d) E= 147^2-94.147+47^2
e) F= 3^24-(27^4+1).(9^6-1)
f) D= (2^2+4^2+...+100^2)-(1^2-3^2+...+99^2)
so sánh E= 1632 + 74x163+372 và F= 1472-94.147+472
\(E=163^2+74\times163+37^2=163^2+2\times163\times37+37^2=\left(163+37\right)^2=200^2\)
\(F=147^2-94\times147+47^2=147^2-2\times147\times47+47^2=\left(147-47\right)^2=100^2\)
\(\frac{E}{F}=\frac{200^2}{100^2}=\left(\frac{200}{100}\right)^2=2^2=4\)
\(E=4F\)
Bài 1:So sánh:
A=1632+74.163+372 và B=1472-94.147+472
Giúp mk nha.Thanks
# Thầy Soobin
\(A=163^2+74.163+37^2\)
\(=163^2+2.37.163+37^2\)
\(=\left(163+37\right)^2=200^2\)
\(B=147^2-94.147+47^2\)
\(=147^2-2.47.147+47^2\)
\(=\left(147-47\right)^2=100^2\)
Vậy A > B
BT1: So sánh các số sau:
a) C=8(3^2+1)(3^4+1)...(3^32+1) và D=3^63
b) E=163^2+74.163+37^2 và F=147^2-94.147+47^2
BT2: Chứng minh rằng các biểu thức sau luôn có giá trị âm với mọi giá trị của x:
a) -x^2+4x-5
b) -20+8x^2-x^4
c) -9x^2+6x-2
Bài 7. Tính nhanh
a/ 498mũ 2
b/ 93. 107
c/ 163 mũ 2+ 74.163 + 37mũ 2
d/ 1995 mũ 2 – 1994.1996
e/ 9 mũ 8.2 mũ 8 – (18mũ 4 – 1)(18 mũ 4+ 1)
f/ 125 mũ 2 - 2. 125. 25 + 25 mũ 2
Bài 8. Rút gọn các biểu thức sau
a/ (x mũ 2+ 3x+ 1)mũ 2 + (3x – 1) mữ 2 – 2(x mũ 2+ 3x+ 1)(3x– 1)
b/ (3x mũ 3+ 3x + 1)(3x mũ 3– 3x +1) – (3xmũ 3+1)mũ 2
c/ (2xmũ2+ 2x + 1)(2xmũ2 – 2x + 1) – (2xmũ 2+ 1)mũ 2
Bài 9. Rút gọn rồi tính giá trị biểu thức
a/ A = (2x + y)mũ 2 - (2x + y) (2x - y)+ y(x - y) vì x= - 2; y= 3.
b/ B = (a - 3b)mũ 2 - (a + 3b)mũ 2 - (a -1)(b -2 ) vì a =1/2; b = -3.
MN GIÚP MIK VS MIK CẦN GẤP
Bài 9:
a) Ta có: \(A=\left(2x+y\right)^2-\left(2x+y\right)\left(2x-y\right)+y\left(x-y\right)\)
\(=4x^2+4xy+y^2-4x^2+y^2-xy-y^2\)
\(=3xy-y^2\)
\(=3\cdot\left(-2\right)\cdot3-3^2=-18-9=-27\)
b) Ta có: \(B=\left(a-3b\right)^2-\left(a+3b\right)^2-\left(a-1\right)\left(b-2\right)\)
\(=a^2-6ab+9b^2-a^2-6ab-9b^2-ab+2a+b-2\)
\(=-13ab+2a+b-2\)
\(=-13\cdot\dfrac{1}{2}\cdot\left(-3\right)+2\cdot\dfrac{1}{2}+\left(-3\right)-2\)
\(=\dfrac{31}{2}\)
Bài 7:
a) \(498^2=\left(500-2\right)^2=250000-2000+4=248004\)
b) \(93\cdot107=100^2-7^2=10000-49=9951\)
c) \(163^2+74\cdot163+37^2=\left(163+37\right)^2=200^2=40000\)
d) \(1995^2-1994\cdot1996=1995^2-1995^2+1=1\)
e) \(9^8\cdot2^8-\left(18^4-1\right)\left(18^4+1\right)\)
\(=18^8-18^8+1=1\)
f) \(125^2-2\cdot125\cdot25+25^2=\left(125-25\right)^2=100^2=10000\)
Bài 8:
a) Ta có: \(\left(x^2+3x+1\right)^2-2\left(x^2+3x+1\right)\left(3x-1\right)+\left(3x-1\right)^2\)
\(=\left(x^2+3x+1-3x+1\right)^2\)
\(=\left(x^2+2\right)^2\)
\(=x^4+4x^2+4\)
b) Ta có: \(\left(3x^3+3x+1\right)\left(3x^3-3x+1\right)-\left(3x^3+1\right)^2\)
\(=\left(3x^3+1\right)^2-9x^2-\left(3x^3+1\right)^2\)
\(=-9x^2\)
c) Ta có: \(\left(2x^2+2x+1\right)\left(2x^2-2x+1\right)-\left(2x^2+1\right)^2\)
\(=\left(2x^2+1\right)^2-4x^2-\left(2x^2+1\right)^2\)
\(=-4x^2\)
Tính nhanh.
a) (-4).(-8).(-17).(-25).125
b) (236 – 362) – (638 + 463)
c) (- 325 – 147) – ( - 625 + 853) – (-96)
d) 69.(- 47) – 31. (- 47)
e) 98. (- 37) + (- 49).126
f) – 35. (49 – 125) – 125 .(35 – 49)
g) 2 + 4 – 6 – 8 + 10 + 12 – 14 – 16 + …+ 90 + 92 – 94 – 96
h) 1 + 3 + 3 2 + 3 3 + ….+ 3 50
Tính nhanh
a. 5/11 + 1/4 + 2/5 + 6/11 + 3/4 + 6/25 + 9/25
b. 19/4 + 37/100 + 1/8 + 1/2 + 163/100 + 3/8
a.
(5/11 + 6/11 ) + ( 1/4 +3/4) + ( 6/25 + 9/25)
= 11/11 + 4/4 + 15/25
= 1 +1 + 3/5
= 2+3/5 = 13/5
b.
( 37/100 + 163/100) + (1/8 + 3/8 ) + 19/4 + 1/2
= 200/100 + 4/8 + ( 19/4 + 2/4)
= 2 + 1/2 + 21/4
= 31/4
19/4+37/100+1/8+1/2+163/100+3/8
\(\frac{19}{4}+\frac{37}{100}+\frac{1}{8}+\frac{1}{2}+\frac{163}{100}+\frac{3}{8}\)
\(=\left(\frac{37}{100}+\frac{163}{100}\right)+\left(\frac{1}{8}+\frac{3}{8}+\frac{1}{2}\right)+\frac{19}{4}\)
\(=2+1+\frac{19}{4}\)
\(=3+\frac{19}{4}\)
\(=\frac{31}{4}\)
\(\frac{19}{4}+\frac{37}{100}+\frac{1}{8}+\frac{1}{2}+\frac{163}{100}+\frac{3}{8}\)
\(=\left(\frac{37}{100}+\frac{163}{100}\right)+\left(\frac{1}{8}+\frac{3}{8}+\frac{1}{2}\right)+\frac{19}{4}\)
\(=\left(\frac{37}{100}+\frac{163}{100}\right)+\left(\frac{1}{8}+\frac{3}{8}+\frac{4}{8}\right)+\frac{19}{4}\)
\(=2+1+\frac{19}{4}\)
\(=3+\frac{19}{4}\)
\(=\frac{31}{4}\)
Tích nha
19/4+37/100+1/8+1/2+163/100+3/8
\(\frac{19}{4}+\frac{37}{100}+\frac{1}{8}+\frac{1}{2}+\frac{163}{100}+\frac{3}{8}\)
\(=\frac{19}{4}+\frac{37}{100}+\frac{163}{100}+\frac{1}{8}+\frac{3}{8}+\frac{1}{2}\)
\(=\frac{19}{4}+2+\frac{1}{2}+\frac{1}{2}\)
\(=\frac{19}{4}+2+1\)
\(=\frac{19}{4}+3\)
\(=\frac{31}{4}\)
\(\frac{19}{4}+\frac{37}{100}+\frac{1}{8}+\frac{1}{2}+\frac{163}{100}+\frac{3}{8}\)
\(=\left(\frac{19}{4}+\frac{1}{2}\right)+\left(\frac{37}{100}+\frac{163}{100}\right)+\left(\frac{1}{8}+\frac{3}{8}\right)\)
\(=\frac{21}{4}+2+\frac{1}{2}\)
\(=5,25+2+0,5\)
\(=7,75\)
Ai k mik mik k lại