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CM
24 tháng 5 2017
Ta có
A = 1 + 15 ( 4 2 + 1 ) ( 4 4 + 1 ) ( 4 8 + 1 ) = 1 + ( 4 2 – 1 ) ( 4 2 + 1 ) ( 4 4 + 1 ) ( 4 8 + 1 ) = 1 + 4 2 2 − 1 4 4 + 1 4 8 + 1 = 1 + 4 4 − 1 4 4 + 1 4 8 + 1 = 1 + 4 4 2 − 1 4 8 + 1 = 1 + 4 8 − 1 4 8 + 1 = 1 + 4 8 2 − 1 = 1 + 4 16 − 1 = 4 16 = 4.4 15 = 2.2.4 15 2 )
V à B = 4 3 5 + 4 5 3 = 4 3.5 + 4 5.3 = 4 15 + 4 15 = 2.4 15
V ì A = 2 . 2 . 4 15 ; B = 2 . 4 15 = > A = 2 B
Đáp án cần chọn là: C
PT
1
CM
10 tháng 9 2019
P = (5x − 1) + 2(1 − 5x)(4 + 5x) + 5 x + 4 2
= 5x – 1 + (2 – 10x).( 4+ 5x) + 5 x + 4 2
= 5x – 1 + 8 + 10x – 40x – 50 x 2 + 25 x 2 + 40x + 16
= (- 50 x 2 + 25 x 2 )+ ( 5x + 10x – 40x + 40x) + (- 1+ 8 + 16)
= -25 x 2 + 15x + 23
CP
2
H9
HT.Phong (9A5)
CTVHS
20 tháng 7 2023
\(2\sqrt{27}-\sqrt{\dfrac{16}{3}}-\sqrt{48}-\sqrt{8\dfrac{1}{3}}\)
\(=6\sqrt{3}-4\sqrt{\dfrac{1}{3}}-4\sqrt{3}-5\sqrt{\dfrac{1}{3}}\)
\(=2\sqrt{3}-9\sqrt{\dfrac{1}{3}}\)
\(=2\sqrt{3}-3\sqrt{9\cdot\dfrac{1}{3}}\)
\(=2\sqrt{3}-3\sqrt{3}\)
\(=-\sqrt{3}\)
________________________
\(\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\)
\(=\left(5\sqrt{5}-2\sqrt{3}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+3\sqrt{3}\right)\)
\(=\left(3\sqrt{5}-2\sqrt{3}\right)\left(3\sqrt{5}+2\sqrt{3}\right)\)
\(=\left(3\sqrt{5}\right)^2-\left(2\sqrt{3}\right)^2\)
\(=15-12\)
\(=3\)
9B
4
21 tháng 12 2017
Ta có: \(\frac{1}{x^2+9x+20}\)\(+\frac{1}{x^2+11x+30}\)\(+\frac{1}{x^2+13x+42}\)
=\(\frac{1}{x^2+4x+5x+20}\)\(+\frac{1}{x^2+5x+6x+30}\)\(+\frac{1}{x^2+6x+7x+42}\)
=\(\frac{1}{x\left(x+4\right)+5\left(x+4\right)}\)\(+\frac{1}{x\left(x+5\right)+6\left(x+5\right)}\)\(+\frac{1}{x\left(x+6\right)+7\left(x+6\right)}\)
=\(\frac{1}{\left(x+4\right)\left(x+5\right)}\)\(+\frac{1}{\left(x+5\right)\left(x+6\right)}\)\(+\frac{1}{\left(x+6\right)\left(x+7\right)}\)
=\(\frac{1}{x+4}-\frac{1}{x+5}\)\(+\frac{1}{x+5}-\frac{1}{x+6}\)\(+\frac{1}{x+6}-\frac{1}{x+7}\)
=\(\frac{1}{x+4}-\frac{1}{x+7}\)
=\(\frac{x+7-x-4}{\left(x+4\right)\left(x+7\right)}\)=\(\frac{3}{\left(x+4\right)\left(x+7\right)}\)
KT
21 tháng 12 2017
\(\frac{1}{x^2+9x+20}\) \(+\) \(\frac{1}{x^2+11x+30}\) \(+\)\(\frac{1}{x^2+13x+42}\)
= \(\frac{1}{\left(x+4\right)\left(x+5\right)}\)\(+\) \(\frac{1}{\left(x+5\right)\left(x+6\right)}\) \(+\) \(\frac{1}{\left(x+6\right)\left(x+7\right)}\)
= \(\frac{1}{x+4}\)\(-\)\(\frac{1}{x+5}\) \(+\)\(\frac{1}{x+5}\)\(-\)\(\frac{1}{x+6}\)\(+\)\(\frac{1}{x+6}\)\(-\)\(\frac{1}{x+7}\)
= \(\frac{1}{x+4}\)\(-\)\(\frac{1}{x+7}\)= \(\frac{x+7-\left(x+4\right)}{\left(x+4\right)\left(x+7\right)}\)= \(\frac{3}{x^2+11x+28}\)
H9
HT.Phong (9A5)
CTVHS
21 tháng 8 2023
Bài 13:
a) \(501^2\)
\(=\left(500+1\right)^2\)
\(=500^2+2\cdot500\cdot1+1^2\)
\(=250000+1000+1\)
\(=251001\)
b) \(88^2+24\cdot88+12^2\)
\(=88^2+2\cdot12\cdot88+12^2\)
\(=\left(88+12\right)^2\)
\(=100^2\)
\(=10000\)
c) \(52\cdot48\)
\(=\left(50+2\right)\left(50-2\right)\)
\(=50^2-2^2\)
\(=2500-4\)
\(=2496\)
Bài 14:
a) \(P=\left(2x-1\right)\left(4x^2+2x+1\right)+\left(x+1\right)\left(x^2-x+1\right)\)
\(P=\left(2x\right)^3-1+x^3+1\)
\(P=8x^3+x^3\)
\(P=9x^3\)
b) \(Q=\left(x-y\right)\left(x^2+xy+y^2\right)-\left(x+y\right)\left(x^2-xy+y^2\right)+2y^3\)
\(Q=x^3-y^3-x^3-y^3+2y^3\)
\(Q=-2y^3+2y^3\)
\(Q=0\)
PN
RÚT GỌN BIỂU THỨC
a) 32(x+2)(x-2)-1/2(6-8x)2 -48
b) (x+9)(x2+27)-(x+3)3
c) (6x+1)2(6x-1)2-2(1+6x)(6x-1)
0
28 tháng 10 2016
a) \(87^2+26\cdot87+13^2=87^2+2\cdot87\cdot13+13^2=\left(87+13\right)^2=100^2=10000\)
Đặt A = (42 + 1)(44 + 1)(48 + 1)...(42016 + 1)
15A = (42 - 1)(42 + 1)(44 + 1)(48 + 1)...(42016 + 1)
15A = (44 - 1)(44 + 1)(48 + 1)...(42016 + 1)
15A = (48 - 1)(48 + 1)...(42016 + 1)
15A = 44032 - 1
\(A=\frac{4^{4032}-1}{15}\)