Question

If
M is equal to 1÷3-2root2
N is equal to 1÷3+2root2 find
m2  , n2 and nm

Answer 1

Answer:

If m = 1 / 3 - 2 root 2 and n = 1 / 3 + 2 root 2 . find = m^2 , n^2 , mn.

Answer 2

Answer:

$m = \frac{1}{3 - 2 \sqrt{ 2} } \\ \\ n = \frac{1}{3 + 2 \sqrt{2} } \\ \\ {m}^{2} = {( \frac{1}{3 - 2 \sqrt{2} } )}^{2} \\ = \frac{1}{9 + 8 - 12 \sqrt{2} }$

${m}^{2} = \frac{1}{17 - 12 \sqrt{2} }$

${n}^{2} = {( \frac{1}{3 + 2 \sqrt{2} } )}^{2} \\ \\ {n}^{2} = \frac{1}{9 + 8 + 12 \sqrt{2} } \\ \\ {n}^{2} = \frac{1}{17 + 12 \sqrt{2} }$

$nm \: = ( \frac{1}{3 + 2 \sqrt{2} } )( \frac{1}{3 - 2 \sqrt{2} } ) \\ \\ = \frac{1}{ {3}^{2} - {(2 \sqrt{2} )}^{2} }$

$= \frac{1}{9 - 8} \\ \\ nm = \frac{1}{1} = 1$