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SMUP 2010

Solusi SMUP 2010 Kode 041 – Nomor 3


Solusi\ dari\ \big(x^2+2\big)^2-5\big(x^2+2\big)\ge 6\ adalah\ .... \\A.\quad x\le -2\,\,\, atau\,\,\, x\ge 2\\B.\quad x\le -1\,\,\, atau\,\,\, x\ge 6\\C.\quad x\le -2\,\,\, atau\,\,\, x\ge 5\\D.\quad x\le -5\,\,\, atau\,\,\, x\ge 2\\E.\quad x\le -1\,\,\, atau\,\,\, x\ge 5
Jawaban: A

\begin{array} {rcl} \big(x^2+2\big)^2-5\big(x^2+2\big)&\ge &6\\\\x^4+4x^2+4-5x^2-10-6&\ge &0\\\\x^4-x^2-12&\ge &0\\\\\big(x^2\big)^2-\big(x^2\big)-12&\ge &0\\\\\big(x^2-4\big) \big(x^2+3\big)&\ge &0\end{array}
sehingga diperoleh:

x^2\le -3\,\,\, atau\,\,\, x^2\ge 4
yang memenuhi adalah:

\begin{array} {rcl} x^2&\ge &4\\\\x^2-4&\ge &0\\\\(x-2)(x+2)&\ge &0\end{array}
sehingga:

x\le -2\,\,\, atau\,\,\, x\ge 2

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