Roboguru

Diketahui . Nilai

Diketahui begin mathsize 14px style 2 to the power of 2 x end exponent plus 2 to the power of negative 2 x end exponent equals 2 end style. Nilai begin mathsize 14px style 2 to the power of x plus 2 to the power of negative x end exponent equals... end style

  1. 1

  2. 2

  3. begin mathsize 14px style square root of 2 end style

  4. 3

  5. begin mathsize 14px style square root of 3 end style

Jawaban:

Misalkan begin mathsize 14px style 2 to the power of x plus 2 to the power of negative x end exponent equals y end style. Selanjutnya dengan mengkuadratkan kedua ruas diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 to the power of x plus 2 to the power of negative x end exponent close parentheses squared end cell equals cell y squared end cell row cell 2 to the power of 2 x end exponent plus 2 times 2 to the power of x times 2 to the power of negative x end exponent plus 2 to the power of negative 2 x end exponent end cell equals cell y squared end cell row cell 2 to the power of 2 x end exponent plus 2 times 2 to the power of x minus x end exponent plus 2 to the power of negative 2 x end exponent end cell equals cell y squared end cell row cell 2 to the power of 2 x end exponent plus 2 to the power of negative 2 x end exponent plus 2 end cell equals cell y squared end cell row 4 equals cell y squared end cell row y equals cell plus-or-minus 2 end cell end table end style

Karena hasil eksponen dengan basis positif, hasilnya tidak mungkin negatif.

Jadi, jawaban yang tepat adalah B.

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