Question

Find the value of $x^3+y^3+z^3-2xyz$, if $x=\sqrt{7}-\sqrt{5},y=\sqrt{5}-\sqrt{3},z=\sqrt{3}-\sqrt{7}$

• A. $2\sqrt{7}-2\sqrt{3}+4\sqrt{5}$
• B. $2\sqrt{7}+2\sqrt{3}+4\sqrt{5}$
• C. $2\sqrt{7}-2\sqrt{3}-4\sqrt{5}$
• D. $2\sqrt{7}+2\sqrt{3}-4\sqrt{5}$

Answer 1

The correct option is D $2\sqrt{7}+2\sqrt{3}-4\sqrt{5}$

as x+y+z=0

$x^3+y^3+z^3=3xyz$

so $x^3+y^3+z^3-2xyz=xyz=(\sqrt{7}-\sqrt{5})(\sqrt{5}-\sqrt{3})(\sqrt{3}-\sqrt{7})=2\sqrt{7}+2\sqrt{3}-4\sqrt{5}$