Pertanyaan

Jika a, b, dan c adalah suku-suku dari barisan geometri, buktikan bahwa: b c + c a + ab a 2 + ab + b 2 = b a

Jika a, b, dan c adalah suku-suku dari barisan geometri, buktikan bahwa:

$\frac{a ^{2} + ab + b ^{2}}{b c + c a + ab} = \frac{a}{b}$

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

terbukti bahwa .

terbukti bahwa $fraction numerator a squared plus a b plus b squared over denominator b c plus c a plus a b end fraction equals a over b$ .

Pembahasan

Misalkan: Maka: Jadi, terbukti bahwa .

Misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row a equals a row b equals cell a r end cell row c equals cell a r squared end cell end table

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a squared plus a b plus b squared over denominator b c plus c a plus a b end fraction end cell equals cell fraction numerator a squared plus a open parentheses a r close parentheses plus open parentheses a r close parentheses squared over denominator open parentheses a r close parentheses open parentheses a r squared close parentheses plus open parentheses a r squared close parentheses a plus a open parentheses a r close parentheses end fraction end cell row blank equals cell fraction numerator a squared plus a squared r plus a squared r squared over denominator a squared r cubed plus a squared r squared plus a squared r end fraction end cell row blank equals cell fraction numerator up diagonal strike a squared end strike down diagonal strike open parentheses r squared plus r plus 1 close parentheses end strike over denominator up diagonal strike a squared end strike r down diagonal strike open parentheses r squared plus r plus 1 close parentheses end strike end fraction end cell row blank equals cell 1 over r times a over a end cell row blank equals cell fraction numerator a over denominator a r end fraction end cell row blank equals cell a over b open parentheses Terbukti close parentheses end cell end table$

Jadi, terbukti bahwa $fraction numerator a squared plus a b plus b squared over denominator b c plus c a plus a b end fraction equals a over b$ .