+619 Solve for $a$: \(\sqrt{4+\sqrt{16+16a}}+ \sqrt{1+\sqrt{1+a}} = 6\)
+129852
Note that
√[ 4 + √ [16 + 16a] ] can be written as
√[ 4 + 4√ [1 + a] ] =
2 √[ 1+ √ [1 + a] ]
Let this = 2x
So we have
2x + x = 6
3x = 6
x = 2
So...
√[ 1+ √ [1 + a] ] = 2 square both sides
1 + √ [1 + a] = 4 subtract 1 from both sides
√ [1 + a] = 3 square both sides again
1 + a = 9 → a = 8
