3/4 = a/128
a = ...
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a) \(\sqrt{4\left(a-3\right)^2}=2\left(a-3\right)=2a-6\)
b) \(\sqrt{a^2\left(a+1\right)^2}=a\left(a+1\right)=a^2+a\)
c) \(\sqrt{\dfrac{16a^4b^6}{128a^6b^6}}=\sqrt{\dfrac{1}{8a^2}}=\dfrac{1}{\sqrt{8}\left|a\right|}=\dfrac{1}{-\sqrt{8}a}=\dfrac{-\sqrt{8}}{8a}\)
a: \(\sqrt{4\left(a-3\right)^2}=2\cdot\left(a-3\right)=2a-6\)
b: \(\sqrt{a^2\left(a+1\right)^2}=a\left(a+1\right)=a^2+a\)
c: \(\dfrac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\sqrt{\dfrac{16a^4b^6}{128a^6b^6}}=\sqrt{\dfrac{1}{8a^2}}=\sqrt{\dfrac{2}{16a^2}}=-\dfrac{\sqrt{2}}{4a}\)
Để 128a chia hết cho 2 thì a E { 0,2,4,6,8 } (1)
Để 128a chia hết cho 3 thì 1 + 2 + 8 + a chia hết cho 3
hay 11 + a chia hết cho 3
hay a E { 1,4,7 } (2)
Từ (1) và (2) => a = 4
Vậy a = 4
\(3\sqrt{2a}-\sqrt{2.3^2a.a^2}-\frac{1}{4}\sqrt{8^2.2a}=3\sqrt{2a}-3a\sqrt{2a}-2\sqrt{2a}=\sqrt{2a}-3a\sqrt{2a}\)
\(\left(1-3a\right)\sqrt{2a}\)
nếu là phương trình :
\(\sqrt{2a}\left(1-3a\right)=0\Leftrightarrow\left(1-3a\right)=0\Leftrightarrow1-3a=0\Leftrightarrow a=\frac{1}{3}\)
\(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\sqrt{\frac{16a^4b^6}{128a^6b^6}}=\sqrt{\frac{1}{8a^2}}=\frac{\sqrt{1}}{\sqrt{8a^2}}=\frac{1}{\sqrt{2}\sqrt{4}\sqrt{a}}\)
=\(\frac{1}{2\sqrt{2}a}\)
\(\dfrac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\sqrt{\dfrac{16a^4b^6}{128a^6b^6}}=\sqrt{\dfrac{1}{8a^2}}=\sqrt{\dfrac{2}{16a^2}}=-\dfrac{\sqrt{2}}{4a}\)
\(\dfrac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\dfrac{4a^2b^3}{8\sqrt{2}a^3b^3}=\dfrac{1}{2\sqrt{2}a}\)
+) Nếu \(a\ge0\) \(\Rightarrow\sqrt{128a^2}=8a\sqrt{2}\)
+) Nếu \(a< 0\) \(\Rightarrow\sqrt{128a^2}=-8a\sqrt{2}\)
ĐKXĐ : \(a,b\ne0\)
\(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\frac{\sqrt{4^2.\left(a^2\right)^2.\left(b^3\right)^2}}{\sqrt{\left(8\sqrt{2}\right)^2.\left(a^3b^3\right)^2}}=\frac{4a^2.\left|b^3\right|}{8\sqrt{2}.\left|a^3b^3\right|}=\frac{a^2}{2\sqrt{2}a^2.\left|a\right|}=\frac{1}{2\sqrt{2}\left|a\right|}\)
Nếu a < 0 thì \(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\frac{1}{-2\sqrt{2}.a}\)
Nếu a > 0 thì \(\frac{\sqrt{16a^4b^6}}{\sqrt{128a^6b^6}}=\frac{1}{2\sqrt{2}.a}\)
\(^2+5=5\left(x+\frac{4}{5}\right)^2+\frac{9}{5}\ge\frac{9}{5}\)
a=128:4x3=96