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Akar-akar persamaan 2 ⋅ 3 2 x − 20 ⋅ 3 x + 18 = 0 adalah x 1 ​ dan x 2 ​ . Nilai x 1 ​ + x 2 ​ = ...

Akar-akar persamaan  adalah  dan . Nilai  = ...

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nilai adalah .

nilai begin mathsize 14px style x subscript 1 plus x subscript 2 end style adalah begin mathsize 14px style 2 end style.

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Pembahasan
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Perhatikan perhitungan berikut. Ingat: Maka: misalkan ,maka: Didapatkan atau sehingga: atau Didapatkan atau . Maka: Jadi, nilai adalah .

Perhatikan perhitungan berikut.

Ingat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of p close parentheses to the power of q end cell equals cell a to the power of p q end exponent end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of f open parentheses x close parentheses end exponent end cell equals cell a to the power of p end cell row cell f open parentheses x close parentheses end cell equals p end table end style

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 times 3 to the power of 2 x end exponent minus 20 times 3 to the power of x plus 18 end cell equals 0 row cell 2 times open parentheses 3 to the power of x close parentheses squared minus 20 times 3 to the power of x plus 18 end cell equals 0 end table end style

misalkan begin mathsize 14px style 3 to the power of x equals p end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 p squared minus 20 p plus 18 end cell equals 0 row cell p squared minus 10 p plus 9 end cell equals 0 row cell open parentheses p minus 9 close parentheses open parentheses p minus 1 close parentheses end cell equals 0 end table end style

Didapatkan begin mathsize 14px style p equals 9 end style atau begin mathsize 14px style p equals 1 end style sehingga:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row p equals 9 row cell 3 to the power of x end cell equals 9 row cell 3 to the power of x end cell equals cell 3 squared end cell row x equals 2 end table end style

atau

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row p equals 1 row cell 3 to the power of x end cell equals 1 row cell 3 to the power of x end cell equals cell 3 to the power of 0 end cell row x equals 0 end table end style

Didapatkan begin mathsize 14px style x subscript 1 equals 2 end style atau begin mathsize 14px style x subscript 2 equals 0 end style. Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell 2 plus 0 end cell row blank equals 2 end table end style

Jadi, nilai begin mathsize 14px style x subscript 1 plus x subscript 2 end style adalah begin mathsize 14px style 2 end style.

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