If \(a = \sqrt {7 + 2\sqrt {12} }\ and\;b = \sqrt {7 - 2\sqrt {12} }\) then find the value if a3 + b3 + a2 + b2 + 1
1). 72
2). 52
3). 67
4). 68
$(\begin{array}{l} a = \sqrt {7 + 2\sqrt {12} } = \sqrt 4 + \sqrt 3 \\ b = \sqrt {7 - 2\sqrt {12} } = \sqrt 4 - \sqrt 3 \end{array})$
a + b = 2√4 = 4
a × b = 1
a3 + b3 + a2 + b2 + 1
⇒ (a + b)3 - 3ab (a + b) + (a + b)2 - 2ab + 1
⇒ 64 - 12 + 16 - 2 + 1 = 67
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