if x=3-root2 show (root x-1÷root x)=+/- 2
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. L. H. S.
X=3-root 2
1/X =3+root 2
Therefore,
(root x - 1/root x) ^2= (root x) ^2+ (root 1/x)^2 - 2*root x*root 1/x. __(1)
=x+1/x - 2 ___(2)
putting here the value of x and 1 / X.
= 3-root 2 +3+root 2 - 2
= 3+3-2
=4
From (1)equation.
(root x - 1/root x) ^2 =4
(root x - 1/root x) =root 4
=+/-2.
=R. H. S.
Hence proved.
X=3-root 2
1/X =3+root 2
Therefore,
(root x - 1/root x) ^2= (root x) ^2+ (root 1/x)^2 - 2*root x*root 1/x. __(1)
=x+1/x - 2 ___(2)
putting here the value of x and 1 / X.
= 3-root 2 +3+root 2 - 2
= 3+3-2
=4
From (1)equation.
(root x - 1/root x) ^2 =4
(root x - 1/root x) =root 4
=+/-2.
=R. H. S.
Hence proved.
navin24:
why you take 1/x=3+root2
!!!!!!!!!
3+root 2 comes by rationalisation of x
x =3-root and 1/x =1÷ 3-root 2 *3+root 2 /3+root 2
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