Pertanyaan

UMPTN 1993 (Rayon C) Jika 2 1 lo g ( 2 x 2 − x − 2 ) = lo g ( x + 2 ) maka nilai maksimum f ( y ) = − y 2 + 4 x y + 5 x 2 sama dengan...

UMPTN 1993 (Rayon C)

Jika $\frac{1}{2} lo g (2 x^{2} - x - 2) = lo g (x + 2)$ maka nilai maksimum $f (y) = - y^{2} + 4 x y + 5 x^{2}$ sama dengan...

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Klaim

H. Janatu

Master Teacher

Mahasiswa/Alumni Universitas Riau

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Jadi, jawaban yang tepat adalah E.

$begin mathsize 14px style 1 half log space left parenthesis 2 x squared minus x minus 2 right parenthesis equals log space left parenthesis x plus 2 right parenthesis log space left parenthesis 2 x squared minus x minus 2 right parenthesis to the power of 1 half end exponent equals log space left parenthesis x plus 2 right parenthesis left parenthesis 2 x squared minus x minus 2 right parenthesis to the power of 1 half end exponent equals space left parenthesis x plus 2 right parenthesis space space left parenthesis k u a d r a t k a n right parenthesis 2 x squared minus x minus 2 equals x squared plus 4 x plus 4 x squared minus 5 x minus 6 equals 0 open parentheses x minus 6 close parentheses open parentheses x plus 1 close parentheses equals 0 x equals 6 x equals negative 1 u n t u k space x equals 6 f left parenthesis y right parenthesis equals negative y squared plus 24 y plus 180 n i l a i space m a x equals negative fraction numerator D over denominator 4 a end fraction equals negative fraction numerator 24 squared minus 4 times left parenthesis negative 1 right parenthesis times 180 over denominator 4 times left parenthesis negative 1 right parenthesis end fraction equals 324 u n t u k space x equals negative 1 f left parenthesis y right parenthesis equals negative y squared minus 4 y plus 5 n i l a i space m a x equals negative fraction numerator D over denominator 4 a end fraction equals negative fraction numerator open parentheses negative 4 close parentheses squared minus 4 times left parenthesis negative 1 right parenthesis times 5 over denominator 4 times left parenthesis negative 1 right parenthesis end fraction equals 9 end style$

Jadi, jawaban yang tepat adalah E.