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a) \(\frac{15^{15}.5^{10}}{9^7.25^{13}}=\frac{3^{15}.5^{15}.5^{10}}{3^{14}.5^{26}}=\frac{3.5^{25}}{5^{26}}=\frac{3}{5}\)
b) \(\sqrt{\frac{4}{81}}:\sqrt{\frac{25}{81}}-1\frac{2}{5}\)
\(=\sqrt{\frac{2^2}{9^2}}:\sqrt{\frac{5^2}{9^2}}-\frac{7}{5}\)
\(=\frac{2}{9}:\frac{5}{9}-\frac{7}{5}\)
\(=\frac{2}{9}.\frac{9}{5}-\frac{7}{5}\)
\(=\frac{2}{5}-\frac{7}{5}\)
\(=\frac{-5}{5}=-1\)
c) \(\left(3^2\right)^2-625+64\)
\(=3^4-625+64\)
\(=81-625+64\)
\(=-480\)
d) \(\frac{\sqrt{3^2}-\sqrt{39^2}}{\sqrt{7^2}-\sqrt{91^2}}\)
\(=\frac{3-39}{7-91}\)
\(=\frac{-36}{-84}\)
\(=\frac{3}{7}\)
C1: Gọi ba số lần lượt là a,b,c
Ta có: \(b=\frac{4}{3}a\Rightarrow4a=3b\Rightarrow\frac{a}{3}=\frac{b}{4}\Rightarrow\frac{a}{9}=\frac{b}{12}\)
\(b=\frac{3}{4}c\Rightarrow4b=3c\Rightarrow\frac{b}{3}=\frac{c}{4}\Rightarrow\frac{b}{12}=\frac{c}{16}\)
\(\Rightarrow\frac{a}{9}=\frac{b}{12}=\frac{c}{16}\Rightarrow\frac{a^2}{81}=\frac{b^2}{144}=\frac{c^2}{256}=\frac{a^2+b^2+c^2}{81+144+256}=\frac{481}{481}=1\)
=> \(\frac{a^2}{81}=1\Rightarrow a^2=81\Rightarrow a=\pm9\)
\(\frac{b^2}{144}=1\Rightarrow b^2=144\Rightarrow b=\pm12\)
\(\frac{c^2}{256}=1\Rightarrow c^2=256\Rightarrow c=\pm16\)
C2: Làm tiếp phần c1
Đặt \(\frac{a}{9}=\frac{b}{12}=\frac{c}{16}=k\Rightarrow a=9k,b=12k,c=16k\)
Ta có: a2 + b2 + c2 = 481
=> (9k)2 + (12k)2 + (16k)2 = 481
=> 81k2 + 144k2 + 256k2 = 481
=> k2(81 + 144 + 256) = 481
=> 481k2 = 481
=> k2 = 1
=> k = \(\pm\)1
Với k = 1 => a = 9, b = 12, c = 16
Với k = -1 => a = -9, b = -12, c = -16
Vậy...
a, \(-\frac{187}{70}\)
b,\(\frac{27}{70}\)
c,\(\frac{53}{14}\)
d,\(\frac{27}{4}\)
e,1
f,\(\frac{23}{4}\)
g,-1
i,6
k,315
l,\(\frac{9}{2}\)
\(\sqrt{\frac{1}{9}+\frac{1}{16}}\)
\(=\frac{1}{3}+\frac{1}{4}\)
\(=\frac{7}{12}\)
a) \(\sqrt{\frac{4}{81}}:\sqrt{\frac{25}{81}}-1\frac{2}{5}\)
\(=\frac{2}{9}:\frac{5}{9}-\frac{7}{5}\)
\(=\frac{2}{5}-\frac{7}{5}\)
\(=-1.\)
b) \(\sqrt{36}.\sqrt{\frac{25}{16}}+\frac{1}{4}\)
\(=6.\frac{5}{4}+\frac{1}{4}\)
\(=\frac{15}{2}+\frac{1}{4}\)
\(=\frac{31}{4}.\)
c) \(1\frac{1}{2}+\frac{4}{7}:\left(-\frac{8}{9}\right)\)
\(=\frac{3}{2}+\frac{4}{7}:\left(-\frac{8}{9}\right)\)
\(=\frac{3}{2}+\left(-\frac{9}{14}\right)\)
\(=\frac{6}{7}.\)
d) \(1,17-0,4.\left(\frac{1}{2}\right)^2-\frac{1}{-5}\)
\(=\frac{117}{100}-\frac{2}{5}.\frac{1}{4}-\left(-\frac{1}{5}\right)\)
\(=\frac{117}{100}-\frac{1}{10}+\frac{1}{5}\)
\(=\frac{107}{100}+\frac{1}{5}\)
\(=\frac{127}{100}.\)
Chúc bạn học tốt!
a, \(\frac{4}{81}:\sqrt{\frac{25}{81}-1\frac{2}{5}}\)
\(\Rightarrow\frac{4}{81}:\frac{5}{9}-\frac{7}{5}\)
\(\Rightarrow\frac{4}{81}.\frac{9}{5}-\frac{7}{5}\)
\(\Rightarrow\frac{4}{9}.\frac{1}{5}-\frac{7}{5}\)
\(\Rightarrow\frac{-59}{45}\)
b,\(\sqrt{36}.\sqrt{\frac{25}{16}+\frac{1}{4}}\)
\(\Rightarrow6.\frac{5}{4}+\frac{1}{4}\)
\(\Rightarrow\frac{15}{2}+\frac{1}{4}\)
\(\Rightarrow\frac{31}{4}\)
c,\(1\frac{1}{2}+\frac{4}{7}:\frac{-8}{9}\)
\(\Rightarrow\frac{3}{2}-\frac{4}{7}.\frac{-8}{9}\)
\(\Rightarrow\frac{3}{2}-\frac{9}{14}\)
\(\Rightarrow\frac{6}{7}\)
d, \(1,17-\left(0,4.\frac{1}{2}\right)^2-\frac{1}{5}\)
\(\Rightarrow\frac{117}{100}-\left(\frac{1}{5}\right)^2-\frac{1}{5}\)
\(\Rightarrow\frac{117}{100}-\frac{1}{25}-\frac{1}{5}\)
\(\Rightarrow\frac{93}{100}\)
a) \(\left(\frac{2^2}{5}\right)+5\frac{1}{2}.\left(4,5-2,5\right)+\frac{2^3}{-4}\)
\(=\frac{4}{5}+\frac{11}{2}.2+\frac{-8}{4}\)
\(=\frac{4}{5}+11-2\)
\(=\frac{4}{5}+9\)
\(=\frac{49}{9}\)
b) \(\left(-2^3\right)+\frac{1}{2}:\frac{1}{8}-\sqrt{25}+\left|-64\right|\)
\(=-8+4-5+64\)
= 55
c) \(\frac{\sqrt{3^2+\sqrt{39}^2}}{\sqrt{91^2}-\sqrt{\left(-7\right)^2}}\)
\(=\frac{\sqrt{9+39}}{91-\sqrt{49}}\)
\(=\frac{\sqrt{48}}{91-7}\)
\(=\frac{4\sqrt{3}}{84}\)
\(=\frac{\sqrt{3}}{41}\)
d) Xem lại đề nhé em!
e) \(\sqrt{25}-3\sqrt{\frac{4}{9}}\)
\(=5-3.\frac{2}{3}\)
= 5 - 2
= 3
h) \(\left(-3^2\right).\frac{1}{3}-\sqrt{49}+\left(5^3\right):\sqrt{25}\)
\(=-9.\frac{1}{3}-7+125:5\)
\(=-3-7+25\)
= 15
mk tra loi roi nen ko lam lai nua
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