Matematika QUIZ #273( x/5 )^-2 = 5/xNilai x adalah brrapa?​

eastonpacochaulv – March 10, 2023

QUIZ #273

( x/5 )^-2 = 5/x

Nilai x adalah brrapa?​

[tex] { \frac{x}{5} }^{ - 2} = \frac{5}{x} \\ \frac{1}{( \frac{x}{5})^{2} } = \frac{5}{x} \\ \frac{1}{ (\frac{ {x}^{2} }{25}) } = \frac{5}{x} \\ \frac{25}{ {x}^{2} } = \frac{5}{x} \\ 25x = 5 {x}^{2} \\ \frac{25x}{5} = {x}^{2} \\ 5x = {x}^{2} \\ 5 = {x}^{2} \div x \\ 5 = {x}^{2} \div {x}^{1} \\ 5 = {x}^{2 - 1} \\ 5 = {x}^{1} \\ \sf \red{5 = x}[/tex]

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Jawaban:

Nilai x adalah 5.

Penjelasan dengan langkah-langkah:

[tex]( \frac{x}{5} ) {}^{ - 2} = \frac{5}{x} \\ ( \frac{5}{x} ) {}^{2} = \frac{5}{x} \\ \frac{25}{ {x}^{2} } = \frac{5}{x} \\ {x}^{2} (5) = x(25) \\ 5 {x}^{2} = 25x \\ 5 {x}^{2} - 25x = 0 \\ 5x(x - 5) = 0 \\ \to x_{1} = 0 (TM) \\ \to x_{2} = 5[/tex]

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