Question

Find value of P and Q

Answer 1

`P= 6 (1)/(7)\\\\</p><p>Q = 4 (2)/(7)`

Step-by-step Explanation

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