Let x,y,z be non-zero real numbers such that x/y+y/z+z/x=7 and y/x+z/y+x/z=9,then x^3/y^3+y^3/z^3+z^3/x^3 -3 is equal to: A 152 - Vedic Math - Squares and Cubes

Question

Let x,y,z be non-zero real numbers such that x/y+y/z+z/x=7 and
y/x+z/y+x/z=9,then x^3/y^3+y^3/z^3+z^3/x^3 -3 is equal to: A 152 b
153 c 154 d 155

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

We have,xz+yx+zy=9        
i andxy+yz+zx=7        
iiSquaring both sides, we getx2y2+y2z2+z2x2+2xy×yz+2yz×zx+2zx×xy=49⇒x2y2+y2z2+z2x2+2xz+yx+zy=49⇒x2y2+y2z2+z2x2+29=49            Using i⇒x2y2+y2z2+z2x2=49-18⇒x2y2+y2z2+z2x2=31                        
iiiSince, a3+b3+c3=a+b+ca2+b2+c2-ab-bc-caSo,x3y3+y3z3+z3x3=xy+yz+zxx2y2+y2z2+z2x2-xy×yz-yz×zx-zx×xy==xy+yz+zxx2y2+y2z2+z2x2-xz+yx+zy=731-9=7×22∴ x3y3+y3z3+z3x3=154Hence, the correct option is C

Hope
this
information will clear
your doubts about the
topic
Regards

Let x,y,z be non-zero real numbers such that x/y+y/z+z/x=7 and y/x+z/y+x/z=9,then x^3/y^3+y^3/z^3+z^3/x^3 -3 is equal to: A. 152 b.153 c. 154 d. 155