Question

1) Solve the following.
If a = √7 - √5, b = √5 - √3,c=√3 - √7 then find the value of a + b + c - 2abc​

Answer 1

• Substitute The Values of a, b and c in a + b + c - 2abc​

$\sf{\left(\sqrt{7}\:-\:\sqrt{5}\right)\:+\:\left(\sqrt{5}\:-\:\sqrt{3}\right)\:+\:\left(\sqrt{3}\:-\:\sqrt{7}\right)\:-\:2\left(\sqrt{7}\:-\:\sqrt{5}\right)\left(\sqrt{5}\:-\:\sqrt{3}\right)\left(\sqrt{3}\:-\:\sqrt{7}\right)}$

$\sf{=\sqrt{7}-\sqrt{5}+\sqrt{5}-\sqrt{3}+\sqrt{3}-\sqrt{7}-2\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{3}-\sqrt{7}\right)}$

$\sf{=\sqrt{7}-\sqrt{5}+\sqrt{5}-\sqrt{3}+\sqrt{3}-\sqrt{7}+8\sqrt{5}-4\sqrt{7}-4\sqrt{3}}$

$\sf{=\sqrt{7}-\sqrt{5}+\sqrt{5}-4\sqrt{3}-\sqrt{7}+8\sqrt{5}-4\sqrt{7}}$

$\sf{=\sqrt{7}+8\sqrt{5}-4\sqrt{3}-\sqrt{7}-4\sqrt{7}}$

$\sf{=-4\sqrt{7}+8\sqrt{5}-4\sqrt{3}}$