Bài 1: Thực hiện phép tính: \(18.{\left( {{{ – 3} \over 2} + {2 \over 3}} \right)^2} – 2\left( { – {1 \over 2}} \right)\left( {{{ – 4} \over 5}} \right) + 2.\)
Bài 2: Tìm x biết:
a) \({x^2} + {2 \over 9} = {5 \over {12}} + {1 \over 4}\)
b) \({3^{x + 1}} + {3^{x + 3}} = 810\)
Baì 3: chứng minh rằng: \({{{9^{11}} – {9^{10}} – {9^9}} \over {639}} \in\mathbb N.\)
Bài 1: \(18.{\left( {{{ – 3} \over 2} + {2 \over 3}} \right)^2} – 2\left( { – {1 \over 2}} \right)\left( {{{ – 4} \over 5}} \right) + 2 \)
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\(= 18.{\left( { – {5 \over 6}} \right)^2} – 2.{1 \over 4}.\left( { – {4 \over 5}} \right) + 2\)
\( = 18.{{25} \over {36}} + {2 \over 5} + 2 \)
\(= {{25} \over 2} + {2 \over 5} + 2 = {{149} \over {10}} = 14,9.\)
Bài 2: a) \({x^2} + {2 \over 9} = {5 \over {12}} + {1 \over 4} \)
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\(\Rightarrow {x^2} = {5 \over {12}} + {1 \over 4} – {2 \over 9}\)
\(\Rightarrow {x^2} = {4 \over 9}\)
\( \Rightarrow x = \pm {2 \over 3}\).
b) \({3^{x + 1}} + {3^{x + 3}} = 810\)
\(\Rightarrow {3^{x + 1}}\left( {1 + {3^2}} \right) = 810\)
\( \Rightarrow {3^{x + 1}} = 810:\left( {1 + {3^2}} \right)\)
\(\Rightarrow {3^{x + 1}} = 81\)
\( \Rightarrow {3^{x + 1}} = {3^4}\)
\(\Rightarrow x + 1 = 4 \Rightarrow x = 3.\)
Bài 3: \({{{9^{111}} – {9^{10}} – {9^9}} \over {639}} = {{{9^9}\left( {{9^2} – 9 – 1} \right)} \over {639}} = {{{9^9}.71} \over {9.71}} \)\(\;= {9^8} \in\mathbb N.\)
