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SIMAK UI 2010

Solusi SIMAK UI 2010 Kode 509 [IPA] – Nomor 7


Jika\ f(x)=-x^n(x-1)^n,\ maka\ f(x^2)+f(x)f(x+1)\ adalah\ ....\\(A)\quad -(x+1)^{n}x^n\\(B)\quad (x^2-1)^n-x^n(x-1)^n\\(C)\quad -x^{2n}(x^2-1)^n-\big[-(x+1)^{n}x^n\big]\\(D)\quad 0\\(E)\quad 1
Jawaban: D

f(x)=-x^n(x-1)^n=-\big[x(x-1)\big]^n
\begin{array} {lcl} f(x^2)+f(x)f(x+1)&=&-\big[x^2(x^2-1)\big]^n+(-)\big[x(x-1)\big]^n(-)\big[(x+1)(x+1-1)\big]^n\\\\&=&-x^{2n}(x^2-1)^n+\big[x(x-1)(x+1)x\big]^n\\\\&=&-x^{2n}(x^2-1)^n+\big[x^2(x^2-1)\big]^n\\\\&=&-x^{2n}(x^2-1)^n+x^{2n}(x^2-1)^n\\\\&=&0\end{array}

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