Question

If a=
3 +V 5/3-V5
and b = 3 - V5/3+V5
find a2 - B2.​

Answer 1

$a^2-b^2$ $= 12\sqrt{5} ({\frac{1}{\sqrt 3} } -1)$

Step-by-step explanation:

Given

$a= 3+\sqrt{\frac{5}{3} } -\sqrt{5}$

$b= 3-\sqrt{\frac{5}{3} } +\sqrt{5}$

We know that

$a^2-b^2$

$=(a+b)(a-b)$

$=( 3+\sqrt{\frac{5}{3} } -\sqrt{5}+ 3-\sqrt{\frac{5}{3} } +\sqrt{5})[3+\sqrt{\frac{5}{3} } -\sqrt{5}-( 3-\sqrt{\frac{5}{3} } +\sqrt{5})]$\

$=( 3+3)[\sqrt{\frac{5}{3} } -\sqrt{5}+\sqrt{\frac{5}{3} } -\sqrt{5}]$

$=6\times 2(\sqrt{\frac{5}{3} } -\sqrt{5})$

$= 12(\sqrt{\frac{5}{3} } -\sqrt{5})$

$= 12\sqrt{5} ({\frac{1}{\sqrt 3} } -1)$