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slamgirl [31]
3 years ago
12

Solve the following inequality for n. Write your answer in simplest form.

Mathematics
1 answer:
ivann1987 [24]3 years ago
5 0

Answer:

15n +8 < -10n-12

Step-by-step explanation:

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Answer:

P= 6 \frac{1}{7}\\\\Q = 4 \frac{2}{7}

Step-by-step Explanation

\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} }  = P+Q\sqrt 2 \\  \\  \frac{(5 + 3 \sqrt{2}) }{(5 - 3 \sqrt{2}) }  \times  \frac{(5 + 3 \sqrt{2}) }{(5   +  3 \sqrt{2} )} = P+Q\sqrt 2 \\  \\  \frac{ {(5 + 3 \sqrt{2} )}^{2} }{ {(5)}^{2}  - (3 \sqrt{2})^{2}  }  = P+Q\sqrt 2 \\  \\ \frac{ {5}^{2} +  {(3 \sqrt{2} )^{2}  + 2.5.3 \sqrt{2} } }{25 - 9 \times 2} = P+Q\sqrt 2 \\  \\\frac{ 25 + 18  + 30 \sqrt{2}  }{25 - 18} = P+Q\sqrt 2 \\  \\\frac{ 43  + 30 \sqrt{2}  }{7} = P+Q\sqrt 2 \\  \\ \frac{43}{7}  +  \frac{30 }{7} \sqrt{2}  = P+Q\sqrt 2 \\  \\ equating \: like \: terms \: on \: both \: sides \\  \\ P =  \frac{43}{7}   \\  \\ \huge \red { \boxed{ P= 6 \frac{1}{7}}}  \\  \\ Q =  \frac{30}{7}  \\  \\ \huge  \orange { \boxed{ Q = 4 \frac{2}{7} }}

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C step by step answer
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