Question

what will be the conjugate of root[ 3+2 root 2]

Answer 1

heya answer is here.........

$given...... \\ 3 + 2 \sqrt{2} \\ cojugate \: is \\ 3 - 2 \sqrt{2}$
hope it helps u

Answer 2

$let \: take \: 3 + 2 \sqrt{2} = {x}^{2} + {y}^{2} + 2xy$
we can understand that it is the square of rational number x and irrational number y. So 2xy=2√2=>
xy=√2 => y=√2/x...(1) and x^2+y^2 =3...(2)then we get => on squaring (1)we get y^2 =2/x^2 . Substitute y^2 in (2), x^2 +2/x^2 =3 let's take x^2 =k =>
$k + \frac{2}{k} = 3 = > on \: multiplying \: by \: k$
$we \: get \: {k}^{2} + 2 = 3k = > {k}^{2} - 3k + 2$
$= 0 = > {k}^{2} - 2k - k + 2 = 0$
$= > k(k - 2) - 1(k - 2) = 0 = >$
$= > (k - 1)(k - 2) = 0 = > k = 1$
$or \: 2$
So x^2=1 or 2=> let's take x square be 1 so y square =2=> y=√2 . Square root of 3+2√2is 1+√2. Hence conjugate of 1+√2 is 1-√2 .