Đáp án+Giải thích các bước giải:
b)
`sqrt(5 + sqrt(7x)) = 2 + sqrt7`
`<=> 5 + sqrt(7x) = 4 + 4sqrt7 +7`
`<=> sqrt(7x) = 6 + 4sqrt7`
`<=> 7x = 36 + 48sqrt7 + 112`
`<=> 7x = 148 + 48sqrt7`
`<=> x = (148 + 48sqrt7)/7`
d)
`1/2 sqrt(x-1) - 3/2sqrt(9x-9) + 24sqrt((x-1)/64) = -17`
`<=> 1/2 sqrt(x-1) - 3/2* 3sqrt(x-1) + 24sqrt((x-1)/64) = -17`
`<=>1/2 sqrt(x-1) - 9/2sqrt(x-1) + 24sqrt((x-1)/64) = -17`
`<=> -4sqrt(x-1) + 24sqrt((x-1)/64) = -17`
`<=> (576(x-1))/64 - 192sqrt((x-1)/64 *(x-1)) + 16(x-1) = 289`
`<=> 9(x-1) - 192 sqrt((x-1)^2/64) + 16x - 16 =289`
`<=> 9x - 9 - 192 * |x-1|/8 + 16x - 16 = 289`
`<=> 9x - 25 - 24 * |x-1| = 289`
`<=> 25x - 24 * |x-1| = 314`
`<=>` $\left[ \begin{array}{l}25x -24(x-1) = 314 ,(x-1\ge0)\\\\25x - 24 (-x+1) = 314, (x-1<0)\end{array} \right.$
`<=>` $\left[ \begin{array}{l}x=290, x \ge1 \\\\ x = \dfrac{338}{49}, x <1\end{array} \right.$
`<=>` $\left[ \begin{array}{l}x = 290\\\\x\in \emptyset\end{array} \right.$
