Rút gọn biểu thức P = (15 / (căn bậc hai 6 + 1) + 4 / (căn bậc hai 6 - 2)
Câu hỏi:
Rút gọn biểu thức P = \[\left( {\frac{{15}}{{\sqrt 6 + 1}} + \frac{4}{{\sqrt 6 - 2}} - \frac{{12}}{{3 - \sqrt 6 }}} \right)\left( {\sqrt 6 + 11} \right)\].
Trả lời:
P = \[\left( {\frac{{15}}{{\sqrt 6 + 1}} + \frac{4}{{\sqrt 6 - 2}} - \frac{{12}}{{3 - \sqrt 6 }}} \right)\left( {\sqrt 6 + 11} \right)\]
P = \[\left( {\frac{{15\left( {\sqrt 6 - 1} \right)}}{{\left( {\sqrt 6 + 1} \right)\left( {\sqrt 6 - 1} \right)}} + \frac{{4\left( {\sqrt 6 + 2} \right)}}{{\left( {\sqrt 6 - 2} \right)\left( {\sqrt 6 + 2} \right)}} + \frac{{12\left( {3 + \sqrt 6 } \right)}}{{\left( {\sqrt 6 - 3} \right)\left( {\sqrt 6 + 3} \right)}}} \right)\left( {\sqrt 6 + 11} \right)\]
P = \[\left( {\frac{{15\left( {\sqrt 6 - 1} \right)}}{5} + \frac{{4\left( {\sqrt 6 + 2} \right)}}{2} + \frac{{12\left( {3 + \sqrt 6 } \right)}}{{ - 3}}} \right)\left( {\sqrt 6 + 11} \right)\]
P = \[\left( {\frac{{15\sqrt 6 - 15}}{5} + \frac{{4\sqrt 6 + 8}}{2} + \frac{{12\sqrt 6 + 36}}{{ - 3}}} \right)\left( {\sqrt 6 + 11} \right)\]
P = \[\left( {3\sqrt 6 - 3 + 2\sqrt 6 + 4 - 4\sqrt 6 - 12} \right)\left( {\sqrt 6 + 11} \right)\]
P = \[\left( {\sqrt 6 - 11} \right)\left( {\sqrt 6 + 11} \right)\]
P = 6 – 112
P = 6 – 121
P = –115.
