Jika (x - 1/x) = 1/2, hitunglah (4x^2+4/x^2)

Jika (x – 1/x) = 1/2, hitunglah (4x^2+4/x^2)

Jawaban:

${4x}^{2} + frac{4}{ {x}^{2} } =9 \$

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Penjelasan dengan langkah-langkah:

$(x - frac{1}{x}) = frac{1}{2} \$

Kedua ruas dikalikan 2

$(x - frac{1}{x}) = frac{1}{2} \ 2(x - frac{1}{x}) = 2(frac{1}{2}) \ (2x - frac{2}{x}) = 1\$

Kuadratkan kedua ruas

$(2x - frac{2}{x})^{2} = {1}^{2} \ {4x}^{2} - 2(2x)( frac{2}{x}) + frac{4}{ {x}^{2} } = 1 \ {4x}^{2} - 8 + frac{4}{ {x}^{2} } = 1 \ {4x}^{2} + frac{4}{ {x}^{2} } = 1 + 8 \ {4x}^{2} + frac{4}{ {x}^{2} } =9$

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Semoga membantu.

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Note:

(a – b)² = a² – 2ab + b²