Đáp án:
\(\begin{array}{l}
a) - 2\sqrt {x - 1} + x\\
b)7\\
c)x = 26
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)DK:x \ge 1\\
H = \dfrac{{\sqrt {x - 1} + \sqrt x + \sqrt {x - 1} - \sqrt x }}{{x - 1 - x}} + \dfrac{{x\left( {\sqrt x - 1} \right)}}{{\sqrt x - 1}}\\
= \dfrac{{2\sqrt {x - 1} }}{{ - 1}} + x\\
= - 2\sqrt {x - 1} + x\\
b)Thay:x = \dfrac{{53}}{{9 - 2\sqrt 7 }}\\
\to H = - 2\sqrt {\dfrac{{53}}{{9 - 2\sqrt 7 }} - 1} + \dfrac{{53}}{{9 - 2\sqrt 7 }}\\
= 7\\
c)H = 16\\
\to - 2\sqrt {x - 1} + x = 16\\
\to x - 16 = 2\sqrt {x - 1} \\
\to {x^2} - 32x + 256 = 4\left( {x - 1} \right)\left( {DK:x \ge 16} \right)\\
\to {x^2} - 36x + 260 = 0\\
\to \left[ \begin{array}{l}
x = 26\\
x = 10\left( l \right)
\end{array} \right.
\end{array}\)
