Question

If a = √6− √5 √6+ √5 = √6+√5 √6− √5 , find the value of a2 + b2 - 2ab.

Answer 1

Answer:

$a^2+b^2-2ab=480$

Step-by-step explanation:

Formula used:

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2+b^2-2ab$

Given:

$a=\frac{\sqrt6-\sqrt5}{\sqrt6+\sqrt5}$

$b=\frac{\sqrt6+\sqrt5}{\sqrt6-\sqrt5}$

$a-b=\frac{\sqrt6-\sqrt5}{\sqrt6+\sqrt5}-\frac{\sqrt6+\sqrt5}{\sqrt6-\sqrt5}$

$a-b=\frac{(\sqrt6-\sqrt5)^2-(\sqrt6+\sqrt5)^2}{(\sqrt6+\sqrt5)(\sqrt6-\sqrt5)}$

$a-b=\frac{(6+5-2\sqrt6\sqrt5)-(6+5+2\sqrt6\sqrt5)}{6-5}$

$a-b=\frac{(11-2\sqrt6\sqrt5)-(11+2\sqrt6\sqrt5)}{1}$

$a-b=11-2\sqrt6\sqrt5-11-2\sqrt6\sqrt5$

$a-b=-4\sqrt6\sqrt5$

$a-b=-4\sqrt{30}$

Now,

$a^2+b^2-2ab$

$=(a-b)^2$

$=(-4\sqrt{30})^2$

$=16*30$

$=480$