Đáp án:
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Câu `3`
`(3x^2 - 51)^{2n} = (-24)^{2n}`
`↔ 3x^2 - 51 =-24`
`↔ 3x^2 = -24 + 51`
`↔ 3x^2 = 27`
`↔ x^2 = 27÷3`
`↔ x^2 = 9`
`↔` \(\left[ \begin{array}{l}x^2=3^2\\x^2=(-3)^2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=3\\x=-3\end{array} \right.\)
Vậy `x=3` hoặc `x=-3`
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Câu `4`
`x + (-31/12)^2 = (49/12)^2 - x = y`
$\bullet$ `x + (-31/12)^2 = (49/12)^2 - x`
`↔ x + 961/144 = 2401/144 - x`
`↔ x + x = 2401/144 - 961/144`
`↔ 2x = (2401 - 961)/144`
`↔ 2x = 10`
`↔ x = 10÷2`
`↔x=5`
$\bullet$ `(49/12)^2 - x = y^2`
`↔ 2401/144 - 5 = y^2`
`↔ y^2 = 1681/144`
`↔` \(\left[ \begin{array}{l}y^2=(\dfrac{41}{12})^2\\y^2=(\dfrac{-41}{12})^2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}y=\dfrac{41}{12}\\y=\dfrac{-41}{12}\end{array} \right.\)
Vậy `x=5` và `y = 41/12` hoặc `y=(-41)/12`
