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\(\frac{13}{42}-\left(\frac{55}{42}-78\right)\left(-\frac{1}{2}\right)^3\)

\(=\frac{13}{42}-\left(\frac{55}{42}-78\right)\left(-\frac{1}{8}\right)\)

\(=\frac{13}{42}+\frac{3221}{42}.\left(-\frac{1}{8}\right)\)

\(=\frac{13}{42}+-\frac{3221}{42}\)

\(=-\frac{1604}{21}\)

Ta có: \(\left(a+2b-3c-d\right)\left(a+2b+3c+d\right)\)

\(=\left[\left(a+2b\right)-\left(3c+d\right)\right]\cdot\left[\left(a+2b\right)+\left(3c+d\right)\right]\)

\(=\left(a+2b\right)^2-\left(3c+d\right)^2\)

\(=a^2+4ab+4b^2-9c^2-6cd-d^2\)

( a + 2b - 3c - d )( a + 2b + 3c + d )

= [ ( a + 2b ) - ( 3c + d ) ][ ( a + 2b ) + ( 3c + d ) ]

= ( a + 2b )² - ( 3c + d )²

= a² + 4ab + 4b² - ( 9c² + 6cd + d² )

= a² + 4ab + 4b² - 9c² - 6cd - d²

2¹⁷⁸ >  5⁷⁶

bạn phải trình bày rõ ra chứ!!!

172x² - 7⁹ : 98³ = 2^-3

<=> 172x² - 7⁹ : ( 2 . 7² )³ = 1/8

<=> 172x² - 7⁹ : ( 2³ . 7⁶ ) = 1/8

<=> 172x² - 7⁹ : 2³ : 7⁶ = 1/8

<=> 172x² - 7³ : 2³ = 1/8

<=> 172x² - ( 7 : 2 )³ = 1/8

<=> 172x² - 343/8 = 1/8

<=> 172x² = 43

<=> x² = 43/172 = 1/4

<=> x = ±1/2

( 12/25 )^x = ( 5/3 )^-2 - ( -3/5 )⁴

<=> ( 12/25 )^x = 9/25 - 81/625

<=> ( 12/25 )^x = 144/625

<=> ( 12/25 )^x = ( 12/25 )²

<=> x = 2

Bài làm:

Ta có: \(\left(\frac{12}{25}\right)^x=\left(\frac{5}{3}\right)^{-2}-\left(-\frac{3}{5}\right)^4\)

\(\Leftrightarrow\left(\frac{12}{25}\right)^x=\frac{9}{25}-\frac{81}{625}\)

\(\Rightarrow\left(\frac{12}{25}\right)^x=\frac{144}{625}\)

\(\Leftrightarrow\left(\frac{12}{25}\right)^x=\left(\frac{12}{25}\right)^2\)

\(\Rightarrow x=2\)

5^x . ( 5³ )² = 625

<=> 5^x . 5⁶ = 625

<=> 5^x+6 = 625

<=> 5^x+6 = 5⁴

<=> x + 6 = 4

<=> x = -2

\(5^x.\left(5^3\right)^2=625\)

\(\Leftrightarrow5^x.5^6=625\)

\(\Leftrightarrow5^x=\frac{1}{5^2}\)

\(\Leftrightarrow x=-2\)

Bài làm:

Ta có: \(x+\left(-\frac{31}{12}\right)^2=\left(\frac{49}{12}\right)^2-x\)

\(\Leftrightarrow2x=\frac{2401}{144}+\frac{961}{144}\)

\(\Leftrightarrow2x=\frac{1681}{72}\)

\(\Rightarrow x=\frac{1681}{144}\)

=> \(y^2=\frac{1681}{144}+\frac{961}{144}=\frac{2642}{144}\)

=> \(y=\pm\frac{\sqrt{2642}}{12}\)