Question

The value of $(52+6\sqrt{43}{)}^{3/2}-(52-6\sqrt{43}{)}^{3/2}$ is

• A. 828
• B. 882
• C. 248
• D. 842

Answer 1

Answer: (A)

${\left[(\sqrt{43}+3{)}^2\right]}^{3/2}-{\left[(\sqrt{43}-3{)}^2\right]}^{3/2}$
$(3+\sqrt{43}{)}^3+(3-\sqrt{43}{)}^3=2\left[{}^3{C}_0\cdot 3^3+{}^3{C}_2\cdot 3(\sqrt{43}{)}^2\right]$
$2[27+9\cdot 43]=2[27+378]=2(414)=828$