Question

${\left(\sqrt{3}+1\right)}^4+{\left(\sqrt{3}-1\right)}^4$ is a/an

• A. rational number
• B. irrational number
• C. negative integer
• D. None of these

Answer 1

Answer: (A)

We have, ${\left(\sqrt{3}+1\right)}^4+{\left(\sqrt{3}-1\right)}^4$
$=2\left({}^4{C}_0{\left(\sqrt{3}\right)}^4+{}^4{C}_2{\left(\sqrt{3}\right)}^2+{}^4{C}_4{\left(\sqrt{3}\right)}^0\right)$
$=2\left(9+18+1\right)=56$.