Kuis Memasukkan x ke fungsi(Soal OSP 2019)f(x)= x⁴+4x³+6x²+4x+10 Maka, [tex]f( \sqrt[4]{5} - 1)[/tex.... Question from @kelvinho018527

E. 14

Penjelasan dengan langkah-langkah:

f(x)= x⁴+4x³+6x²+4x+10

x = $\sqrt[4]{5}$ -1

supaya lebih mudah, kita bagi-bagi dulu persamaan tersebut dalam beberapa bagian.

$\:$

$\begin{array}{l}{x}^{4} \\ = {( \sqrt[4]{5} - 1 )}^{4} \\ = {( {5}^{ \frac{1}{4} } - 1 )}^{4} \\ = ( {5}^{ \frac{1}{4} } - 1 ) ( {5}^{ \frac{1}{4} } - 1 )( {5}^{ \frac{1}{4} } - 1 )( {5}^{ \frac{1}{4} } - 1 )\\ = ( {5}^{ \frac{1}{4} } ) {}^{4} + {}_{4}C_{3}. ({5}^{ \frac{1}{4} } ) {}^{3} ( - 1) + {}_{4}C_{2}. ({5}^{ \frac{1}{4} } ) {}^{2} ( - 1) {}^{2} + {}_{4}C_{1}. ({5}^{ \frac{1}{4} } ) {}^{1} ( - 1) {}^{3} + ( - 1) {}^{4} \\ = 5 - 4.{5}^{ \frac{3}{4} } + 6. {5}^{ \frac{1}{2} } - 4. {5}^{ \frac{1}{4} } + 1 \\ = - 4 \sqrt[4]{125} + 6 \sqrt{5} - 4 \sqrt[4]{5}+6 \end{array}$

$\:$

$\begin{array}{l} 4x^{3} \\= 4( {5}^{ \frac{1}{4} } - 1 ) {}^{3} \\ = 4( {5}^{ \frac{1}{4} } - 1 ) ( {5}^{ \frac{1}{4} } - 1 )( {5}^{ \frac{1}{4} } - 1 )\\ = 4(( {5}^{ \frac{1}{4} } ) {}^{3} + {}_{3}C_{2}.( {5}^{ \frac{1}{4} } ) {}^{2} .( - 1) + {}_{3}C_{1}.( {5}^{ \frac{1}{4} } ) {}^{1} .( - 1) {}^{2} + ( - 1) {}^{3} ) \\ =4( {5}^{ \frac{3}{4} } - 3. {5}^{ \frac{1}{2} } + 3. {5}^{ \frac{1}{4} } - 1) \\ = 4 \sqrt[4]{125} - 12 \sqrt{5} + 12 \sqrt[4]{5} - 4\end{array}$

$\:$

$\begin{array}{l}6x^{2}\\=6( {5}^{ \frac{1}{4} } - 1) {}^{2} \\ = 6( ({5}^{ \frac{1}{4}} ) {}^{2} - 2. {5}^{ \frac{1}{4} } + 1) \\ = 6 \sqrt{5} - 12 \sqrt[4]{5} + 6 \end{array}$

$\:$

$\begin{array}{l}4x \\=4( \sqrt[4]{5} - 1) \\ = 4 \sqrt[4]{5} - 4\end{array}$

$\:$

MAKA,

$f( \sqrt[4]{5} - 1)$

adalah:

$\begin{array}{l} f( \sqrt[4]{5} - 1) \\ = ( - 4 \sqrt[4]{125} + 6 \sqrt{5} - 4 \sqrt[4]{5}+6) + (4 \sqrt[4]{125} - 12 \sqrt{5} + 12 \sqrt[4]{5} - 4) + (6 \sqrt{5} - 12 \sqrt[4]{5} + 6) + (4 \sqrt[4]{5} - 4) + 10 \\ = 14 \end{array}$

2 votes Thanks 2

kelvinho018527 jawabannya bukan itu

kelvinho018527 coba diteliti lagi

farahashari udah

farahashari maaf kurang teliti tadi di Combinasi nya

kelvinho018527 betul

kelvinho018527 cuma ada cara cepat, perhatikan bentuk itu dimanipulasi jadi (x+1)^4 + 9, masukkan aja, dapat 14

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