Tính:
\(\left(30^2+28^2+29^2+....+4^2+2^2\right)-\left(29^2+27^2+25^2+....+3^2+1^2\right)\)
Những câu hỏi liên quan
Tính nhanh:\(\left(32^2-1^2\right)+\left(34^2-3^2\right)+\left(36^2-5^2\right)+...+\left(56^2-25^2\right)+\left(58^2-27^2\right)+\left(60^2-29^2\right)\)
Bạn dựa vào công thức
a2 - n2 = (a + n)(a - n)
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Giả sử cho biểu thức :
\(T\left(x\right)=\left(1+x^2\right)^{15}=a_0+a_1x+a_2x^2+a_3x^3+.....+a_{29}x^{29}+a_{30}x^{30}.\)
Tính giá trị của biểu thức:
\(H=-2a_1+2^2a_2-2^3a_3+2^4a_4-2^5a_5+...+2^{28}a_{28}-2^{29}a_{29}+2^{30}a_{30}\)
Ta có:
\(T\left(-2\right)=a_0-2a_1+2^2a_2-...-2^{29}a_{29}+2^{30}a_{30}=a_0+H=\left(1+4\right)^{15}\)
\(\Leftrightarrow1+H=5^{15}\)
\(\Leftrightarrow H=5^{15}-1\)
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Tính giá trị biểu thức sau:1/ frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}.2/ frac{5.left(2^2.3^2right)^9.left(2^2right)^6-2.left(2^2.3right)^{14}.3^6}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}3/ frac{2^{12}.13+2^{12}.65}{2^{10}.104}+frac{3^{10}.11+3^{10}.5}{3^9.2^4}4/ frac{5.4^{15}-9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}5/ frac{13.4^6.left(28frac{7}{13}-27frac{5}{18}right)}{59.2^{12}left(frac{5}{14}+frac{5}{84}+frac{5}{204}+frac{5}{374}right)}Tặng người giải mỗi ngày ba điểm hđ ...
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Tính giá trị biểu thức sau:
1/ \(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\).
2/ \(\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^6}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)
3/ \(\frac{2^{12}.13+2^{12}.65}{2^{10}.104}+\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
4/ \(\frac{5.4^{15}-9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
5/ \(\frac{13.4^6.\left(28\frac{7}{13}-27\frac{5}{18}\right)}{59.2^{12}\left(\frac{5}{14}+\frac{5}{84}+\frac{5}{204}+\frac{5}{374}\right)}\)
Tặng người giải mỗi ngày ba điểm hđ :)
1/ \(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\frac{5^{20}.3^{29}-3^{31}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{19}}=\frac{3^{29}.5^{18}.\left(25-9\right)}{3^{29}.5^{18}.\left(7-5\right)}=\frac{16}{2}=8\)
CÁC BÀI CÒN LẠI TƯƠNG TỰ HẾT NHÉ E
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Phân tích đa thức thành nhân tử:
23). left(2a-bright)^2-4left(a-bright)^2
24). 9left(a+bright)^2-4left(a-2bright)^2
25). 4left(2a-bright)^2-16left(a-bright)^2
26). 36left(x-yright)^2-25left(2x-1right)^2
27). left(x^2+1right)^2-4x^2
28). 16x^2-left(x^2+4right)
29). left(4x^2+dfrac{1}{4}right)-4x^2
30). left(4x^2+1right)^2-16x^2
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Phân tích đa thức thành nhân tử:
23). \(\left(2a-b\right)^2-4\left(a-b\right)^2\)
24). \(9\left(a+b\right)^2-4\left(a-2b\right)^2\)
25). \(4\left(2a-b\right)^2-16\left(a-b\right)^2\)
26). \(36\left(x-y\right)^2-25\left(2x-1\right)^2\)
27). \(\left(x^2+1\right)^2-4x^2\)
28). \(16x^2-\left(x^2+4\right)\)
29). \(\left(4x^2+\dfrac{1}{4}\right)-4x^2\)
30). \(\left(4x^2+1\right)^2-16x^2\)
23: \(=\left(2a-b\right)^2-\left(2a-2b\right)^2\)
\(=\left(2a-b-2a+2b\right)\left(2a-b+2a-2b\right)\)
\(=b\left(4a-3b\right)\)
24: \(=\left(3a+3b\right)^2-\left(2a-4b\right)^2\)
\(=\left(3a+3b-2a+4b\right)\left(3a+3b+2a-4b\right)\)
\(=\left(a+7b\right)\left(5a-b\right)\)
25: \(=\left(4a-2b\right)^2-\left(4a-4b\right)^2\)
\(=\left(4a-2b-4a+4b\right)\left(4a-2b+4a-4b\right)\)
\(=2b\left(8a-6b\right)\)
=4b(4a-3b)
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1 tháng 2 2021 lúc 16:23
Tính giá trị biểu thức : A= \(\dfrac{5\left(2^2.3^2\right)^9.\left(2^2\right)^6-2\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
Ta có: \(A=\dfrac{5\cdot\left(2^2\cdot3^2\right)^9\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}\cdot3^4}{5\cdot2^{28}\cdot3^{18}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{5\cdot2^{18}\cdot3^{18}\cdot2^{12}-2\cdot2^{28}\cdot3^{14}\cdot3^4}{5\cdot2^{28}\cdot3^{18}-7\cdot2^{28}\cdot3^{18}\cdot2}\)
\(=\dfrac{5\cdot2^{30}\cdot3^{18}-2\cdot2^{28}\cdot3^{18}}{2^{28}\cdot3^{18}\cdot\left(5-7\cdot2\right)}\)
\(=\dfrac{2^{28}\cdot3^{18}\cdot\left(5\cdot2^2-2\right)}{2^{28}\cdot3^{18}\cdot\left(5-14\right)}\)
\(=\dfrac{20-2}{-9}=\dfrac{18}{-9}=-2\)
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chứng minh cho biểu thức
\(\frac{\left(1^6-29^3\right)\left(2^6-28^3\right)\left(3^6-27^3\right).....\left(10^6-20^3\right)}{\left(1^6+29^3\right)\left(2^6+28^3\right)\left(3^6+27^3\right).....\left(10^6+20^3\right)}=0\)\(0\)
\(5^6-25^3=\left(5^2\right)^3-25^3=25^3-25^3=0\)
\(\Rightarrow\frac{\left(1^6-29^3\right)\left(2^6-28^3\right)\left(3^6-27^3\right)\left(4^6-26^3\right)\left(5^6-25^3\right).....\left(10^6-20^3\right)}{\left(1^6+29^3\right)\left(2^6+28^3\right)\left(3^6+27^3\right)\left(4^6+26^3\right)\left(5^6+25^3\right).....\left(10^6+20^3\right)}=0\)
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A=\(\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
Tính A
\(A=\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^{14}}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
\(A=\frac{5.\left(2^2\right)^9.\left(3^2\right)^9.\left(2^2\right)^6-2.\left(2^2\right)^{14}.3^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
\(A=\frac{5.2^{18}.3^{18}.2^{12}-2.2^{28}.3^{18}}{5.2^{28}.3^{18}-7.2.2^{28}.3^{18}}\)
\(A=5.\frac{\left(2^{18}.2^{12}\right).3^{18}.2^{29}.3^{18}}{2^{28}.3^{18}.\left(5-7-2\right)}\)
\(A=\frac{5.2^{30}.3^{18}-2^{29}.3^{18}}{2^{28}.3^{18}.\left(-9\right)}\)
\(A=\frac{5.2.2^{29}.3^{18}-2^{29}.3^{18}}{2^{28}.3^{18}.\left(-9\right)}\)
\(A=\frac{2^{20}.2^{18}.\left(5.2-1\right)}{2^{28}.3^{18}.\left(-9\right)}\)
\(A=\frac{2^{29}.3^{18}.9}{2^{28}.3^{18}.\left(-9\right)}\)
\(A=\frac{2.11}{11.\left(-2\right)}\)
\(A=-2\)
Vậy : A = -2
tính B = \(\frac{5.\left(2^9.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^4}{5.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
tính nhanh
\(B=1.4+2.5+3.6+...+20.23+30^2+29^2+28^2+27^2+26^2-\left(10^2+11^2+12^2+13^2+14^2\right)\)