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Tunjukkan bahwa, jika a,b, c,x adalah bilangan rea...

Tunjukkan bahwa, jika a,b, c,x adalah bilangan real dan begin mathsize 14px style open parentheses a squared plus b squared close parentheses x squared minus 2 b open parentheses a plus c close parentheses x plus open parentheses b squared plus c squared close parentheses equals 0 end style, maka a,b, dan c merupakan barisan geometri dengan x sebagai rasionya.

Jawaban:

begin mathsize 14px style b squared equals a c a equals U subscript 1 equals a b equals U subscript 2 equals a r c equals U subscript 3 equals a r squared r equals x open parentheses a squared plus b squared close parentheses x squared minus 2 b open parentheses a plus c close parentheses x plus open parentheses b squared plus c squared close parentheses equals 0 x subscript 1 plus x subscript 2 equals fraction numerator 2 b left parenthesis a plus c right parenthesis over denominator a squared plus b squared end fraction equals fraction numerator 2 square root of a c end root open parentheses a plus c close parentheses over denominator a squared plus a c end fraction equals fraction numerator 2 times a r. open parentheses a plus a r squared close parentheses over denominator a squared plus a squared r squared end fraction equals fraction numerator 2 a squared r open parentheses 1 plus r squared close parentheses over denominator a squared left parenthesis 1 plus r squared right parenthesis end fraction equals 2 r r plus r equals 2 r x subscript 1 times x subscript 2 equals fraction numerator b squared plus c squared over denominator a squared plus b squared end fraction equals fraction numerator a c plus c squared over denominator a squared plus a c end fraction equals fraction numerator c open parentheses a plus c close parentheses over denominator a open parentheses a plus c close parentheses end fraction equals c over a equals fraction numerator a r squared over denominator a end fraction equals r squared r times r equals r squared end style 

benar bahwa, jika a,b, c,x adalah bilangan real dan begin mathsize 14px style open parentheses a squared plus b squared close parentheses x squared minus 2 b open parentheses a plus c close parentheses x plus open parentheses b squared plus c squared close parentheses equals 0 end style, maka a,b, dan c merupakan barisan geometri dengan x sebagai rasionya.

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