If x=√5−2√5+2, y=√5+2√5−2 and y2 is (161+72√m), then value of m is ___.
We have x=√5−2√5+2 and y=√5+2√5−2
Rationalizing the denominator gives,
y=√5+2√5−2×√5+2√5+2
y=5+4+4√55−4 (By applying the identities)
y=9+4√51
y2=(9+4√5)(9+4√5)
=81+16×5+72√5
=161+72√5
Comparing this with y2=161+72√m, we get m=5.