Câu hỏi

Chứng minh với mọi t ∈ [ − 1 ; 1 ] ta có

Chứng minh với mọi $t \in [- 1; 1]$ ta có

display style square root of 1 plus straight t end root plus square root of 1 minus straight t end root greater or equal than 1 plus square root of 1 minus straight t to the power of 2 end exponent end root greater or equal than 2 minus straight t to the power of 2 end exponent

R. Robo.Ctvx30

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Giải thích

display style text Có: end text not stretchy left parenthesis square root of 1 plus t end root plus square root of 1 minus t end root not stretchy right parenthesis to the power of 2 end exponent equals 2 plus 2 square root of 1 minus t to the power of 2 end exponent end root

display style text Lại có end text 0 less or equal than 1 minus straight t to the power of 2 end exponent less or equal than 1 comma straight for all straight t element of not stretchy left square bracket negative 1 semicolon 1 not stretchy right square bracket

display style not stretchy rightwards double arrow square root of 1 minus t to the power of 2 end exponent end root greater or equal than 1 minus t to the power of 2 end exponent not stretchy rightwards double arrow 1 plus square root of 1 minus t to the power of 2 end exponent end root greater or equal than 2 minus t to the power of 2 end exponent

display style text (đẳng thức xảy ra end text not stretchy left right double arrow 1 minus t to the power of 2 end exponent equals 0 text hoặc end text 1 not stretchy left right double arrow t equals 0 semicolon plus-or-minus 1 text ). end text