Đáp án:
$a. x = 81$
$b. x = \frac{1025}{64}$
Giải thích các bước giải:
$a. \sqrt[]{25x} - \sqrt[]{16x} = 9$ $( x ≥ 0 )$
⇔ $5\sqrt[]{x} - 4\sqrt[]{x} = 9$
⇔ $\sqrt[]{x} = 9$
⇔ $x = 81$ (TM)
$b. \sqrt[]{16x+16} - \sqrt[]{9x+9} + \sqrt[]{4x-4} + \sqrt[]{x+1} = 16$ $( x ≥ 1 )$
⇔ $\sqrt[]{16(x+1)} - \sqrt[]{9(x+1)} + \sqrt[]{4(x-1)} + \sqrt[]{x+1} = 16$
⇔ $4\sqrt[]{x+1} - 3\sqrt[]{x+1} + 2\sqrt[]{x-1} + \sqrt[]{x+1} = 16$
⇔ $2\sqrt[]{x+1} + 2\sqrt[]{x-1} = 16$
⇔ $\sqrt[]{x+1} + \sqrt[]{x-1} = 8$
⇔ $\sqrt[]{x+1} = 8 - \sqrt[]{x-1}$ $( \sqrt[]{x-1} ≤ 8 ⇔ 1 ≤ x ≤ 65 )$
⇔ $x + 1 = ( 8 - \sqrt[]{x-1} )^{2}$
⇔ $x + 1 = 64 - 16\sqrt[]{x-1} + x - 1$
⇔ $16\sqrt[]{x-1} = 62$
⇔ $8\sqrt[]{x-1} = 31$
⇔ $64( x - 1 ) = 961$
⇔ $x - 1 = \frac{961}{64}$
⇔ $x = \frac{1025}{64}$ (TM)
