Square root
VBT
Calculator
magnet

Câu hỏi

Giải bất phương trình

Giải bất phương trình

log subscript left parenthesis square root of x plus 2 end root minus square root of x right parenthesis end subscript invisible function application 2 less or equal than log subscript square root of x plus 1 end root end subscript invisible function application 2

R. Roboctvx97

Giáo viên

Xác nhận câu trả lời

Giải thích

Ta có ⇔ x > 4 1 ​ Nếu lo g 2 ​ ( x + 2 ​ − x ​ ) > 0 thì lo g 2 ​ x + 1 ​ ≤ lo g 2 ​ ( x + 2 ​ − x ​ ) Với lo g 2 ​ ( x + 2 ​ − x ​ ) > lo g 2 ​ 1 ⇔ ⇔ ⇔ ​ x + 2 ​ > x + 2 > x + 2 0 < x < 4 1 ​ ​ Với lo g 2 ​ x + 1 ​ ≤ lo g 2 ​ ( x + 2 ​ − x ​ ) ⇔ x + 1 ≤ x + 2 − 2 x ( x + 2 ) ​ + x ⇔ 2 x ( x + 2 ) ​ ≤ x + 1 ⇔ 4 x 2 + 8 x ≤ x 2 + 2 x + 1 3 x 2 + 6 x − 1 ≤ 0 0 < x ≤ 3 − 3 + 12 ​ ​

Ta có begin mathsize 12px style table row cell fraction numerator 1 over denominator log subscript 2 invisible function application left parenthesis square root of x plus 2 end root minus square root of x right parenthesis end fraction less or equal than fraction numerator 1 over denominator log subscript 2 invisible function application square root of x plus 1 end root end fraction end cell row cell table attributes columnalign right end attributes row cell open parentheses log subscript 2 invisible function application left parenthesis square root of x plus 2 end root minus square root of x right parenthesis not equal to 0 close parentheses end cell end table end cell row cell text  Với  end text blank x greater than 0 text  thì  end text square root of x plus 1 end root greater than 1 rightwards double arrow log subscript 2 invisible function application square root of x plus 1 end root greater than 0 end cell row cell text  * Néu  end text log subscript 2 invisible function application left parenthesis square root of x plus 2 end root minus square root of x right parenthesis less than 0 text  thì vé trái của  end text left parenthesis 2 right parenthesis less than 0 text , vé phả  end text greater than 0 end cell row cell text  nên (2) luón dúng. Khi dó:  end text end cell row cell    log subscript 2 invisible function application left parenthesis square root of x plus 2 end root minus square root of x right parenthesis less than log subscript 2 invisible function application 1 end cell row cell left right double arrow blank square root of x plus 2 end root minus square root of x less than 1 end cell row cell left right double arrow blank square root of x plus 2 end root less than square root of x plus 1 end cell row cell left right double arrow blank x plus 2 less than x plus 2 square root of x plus 1 end cell end table end style

Nếu  thì 

Với 

Với 

1

Câu hỏi tương tự

Giải phương trình lo g x ​ x + 2 3 x + 2 ​ > 1 ( 1 )

0

Xác nhận câu trả lời

THÔNG TIN

TẢI MIỄN PHÍ ỨNG DỤNG