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Câu hỏi

Biết rằng nếu x ∈ R thỏa mãn 2 7 x + 2 7 − x = 4048 thì 3 x + 3 − x = 9 a + b trong đó a , b ∈ N ; 0 < a ≤ 9 . Tổng a + bbằng

Biết rằng nếu  thỏa mãn  thì

  trong đó .

Tổng a + b bằng

  1. 7

  2. 6

  3. 5

  4. 8

R. Robo.Ctvx44

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Giải thích

- Ta có: 2 7 x + 2 7 − x = 4048 ⇔ ( 3 x ) 3 + ( 3 − x ) 3 = 4048 Vậy a + b = 8

- Ta có: 

table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy left right double arrow open parentheses 3 to the power of x plus 3 to the power of negative x end exponent close parentheses cubed minus 3 open parentheses 3 to the power of x plus 3 to the power of negative x end exponent close parentheses 3 to the power of x 3 to the power of negative x end exponent minus 4048 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell row cell not stretchy left right double arrow open parentheses 3 to the power of x plus 3 to the power of negative x end exponent close parentheses cubed minus 3 open parentheses 3 to the power of x plus 3 to the power of negative x end exponent close parentheses minus 4048 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell row cell not stretchy left right double arrow 3 to the power of x plus 3 to the power of negative x end exponent equals 16. space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end cell row cell text  Với  end text open curly brackets table attributes columnspacing 1em end attributes row cell a comma b element of straight natural numbers end cell row cell 0 less than a less or equal than 9 end cell row cell 9 a plus b equals 16 end cell end table text  , suy ra  end text open curly brackets table attributes columnspacing 1em end attributes row cell a equals 1 end cell row cell b equals 7 end cell end table close text end text close end cell end table

Vậy a + b = 8

1

Câu hỏi tương tự

Giải các phương trình sau trên tập hợp các số thực: x 4 − 6 x 3 + 6 x 2 + 9 x = 2 ( x 2 − 3 x ) ​

0

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