Question

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find m²

Answer 1

m = `1/[ 3 - 2sqrt2 ]`

m = `1/[ 3 - 2sqrt2 ] xx [ 3 + 2sqrt2 ]/[ 3 + 2sqrt2 ]`

m = `[ 3 + 2sqrt2 ]/[ (3)^2 - (2sqrt2)^2 ]`

m = `[ 3 + 2sqrt2 ]/[ 9 - 8 ]`

m = 3 +2√2

⇒ m² = ( 3 + 2√2)²

           = (3)² + 2 x 3 x 2√2 + (2√2)²

           = 9 + 12√2  + 8

           = 17 + 12√2