Đáp án:

\(\eqalign{ & a)\,\,\left( { - 15;3} \right) \cr & b)\,\,x = 2 \cr & c)\,\,vo\,\,nghiem \cr & d)\,\,vo\,\,nghiem \cr & e)\,\,\left[ \matrix{ x = {{14} \over 5} \hfill \cr x = - {{16} \over 5} \hfill \cr} \right. \cr & f)\,\,\left[ \matrix{ x = 3 \hfill \cr x = - 7 \hfill \cr} \right. \cr & g)\,\,x = - 1 \cr & h)\,\,\left[ \matrix{ x = {{17} \over 2} \hfill \cr x = - {{11} \over 2} \hfill \cr} \right. \cr} \)

Giải thích các bước giải:

\(\eqalign{ & a)\,\,{\left( {x + 15} \right)^{200}} + \left| {y - 3} \right| = 0 \cr & Ta\,\,co:\,\,\left\{ \matrix{ {\left( {x + 15} \right)^{200}} \ge 0 \hfill \cr \left| {y - 3} \right| \ge 0 \hfill \cr} \right. \Rightarrow {\left( {x + 15} \right)^{200}} + \left| {y - 3} \right| \ge 0 \cr & Dau\,\,'' = ''\,\,xay\,\,ra \Leftrightarrow \left\{ \matrix{ {\left( {x + 15} \right)^{200}} = 0 \hfill \cr \left| {y - 3} \right| = 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ x + 15 = 0 \hfill \cr y - 3 = 0 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{ x = - 15 \hfill \cr y = 3 \hfill \cr} \right. \cr & \Rightarrow Nghiem:\,\,\left( {x;y} \right) = \left( { - 15;3} \right) \cr & b)\,\,{\left( {x - 1} \right)^{x + 2}} = {\left( {x - 1} \right)^{ - x + 6}} \cr & \Leftrightarrow {{{{\left( {x - 1} \right)}^{x + 2}}} \over {{{\left( {x - 1} \right)}^{ - x + 6}}}} = 1 \cr & \Leftrightarrow {\left( {x - 1} \right)^{x + 2 + x - 6}} = 1 \cr & \Leftrightarrow {\left( {x - 1} \right)^{2x - 4}} = 1 \cr & \Leftrightarrow \left[ \matrix{ x - 1 = 1 \hfill \cr 2x - 4 = 0 \hfill \cr} \right. \Leftrightarrow x = 2 \cr & c)\,\,\left| {5 - 3x} \right| + {2 \over 5} = {1 \over 6} \cr & \Leftrightarrow \left| {5 - 3x} \right| = {1 \over 6} - {2 \over 5} = - {7 \over {30}} < 0\,\,\left( {vo\,\,nghiem} \right) \cr & d)\,\,{1 \over 5} - \left| {{1 \over 5} - x} \right| = 1 \cr & \Leftrightarrow \left| {{1 \over 5} - x} \right| = {1 \over 5} - 1 = - {4 \over 5} < 0\,\,\left( {Vo\,\,nghiem} \right) \cr & e)\,\,{\left( {x + {1 \over 5}} \right)^4} = 81 \cr & \Leftrightarrow {\left( {x + {1 \over 5}} \right)^4} = {3^4} \cr & \Leftrightarrow \left[ \matrix{ x + {1 \over 5} = 3 \hfill \cr x + {1 \over 5} = - 3 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = 3 - {1 \over 5} = {{14} \over 5} \hfill \cr x = - 3 - {1 \over 5} = - {{16} \over 5} \hfill \cr} \right. \cr & f)\,\,{\left( {x + 2} \right)^2} = 25 \cr & \Leftrightarrow {\left( {x + 2} \right)^2} = {5^2} \cr & \Leftrightarrow \left[ \matrix{ x + 2 = 5 \hfill \cr x + 2 = - 5 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = 3 \hfill \cr x = - 7 \hfill \cr} \right. \cr & g)\,\,{3^{x + 5}} = 81 \cr & \Leftrightarrow {3^{x + 5}} = {3^4} \cr & \Leftrightarrow x + 5 = 4 \cr & \Leftrightarrow x = - 1 \cr & h)\,\,17 - \left| {2x - 3} \right| = 3 \cr & \Leftrightarrow \left| {2x - 3} \right| = 17 - 3 = 14 \cr & \Leftrightarrow \left[ \matrix{ 2x - 3 = 14 \hfill \cr 2x - 3 = - 14 \hfill \cr} \right. \cr & \Leftrightarrow \left[ \matrix{ 2x = 17 \hfill \cr 2x = - 11 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{ x = {{17} \over 2} \hfill \cr x = - {{11} \over 2} \hfill \cr} \right. \cr} \)