NDA2016MathematicsBasics of MathematicsActual
If x^ ( y z ) y^ (X z)^2 z^ ( x y ) =y^ 4 y for any x 1, y 1 and z 1 , then which one of the following is correct?
Options
- An y is the GM of nx , nx , nx and nz
- Bn y is the A M of nx , nx , nx and n z
- Cn y is the HM of nx , n x and nz
- Dn y is the AM of n , In x , n z and n z
Correct answer
B. n y is the A M of nx , nx , nx and n z
Step-by-step solution
x^ ( y z ) y^ (x z)^2 z^ ( x y ) =y^ 4 y aligned & [x^ ( y z ) ]+ [y^ (x z)^2 ]+ [z^ ( x y ) ]= [y^ 4 y ] & [ ( y z ) x ]+[2 (x z) y]+ [ ( x y ) z ]=4[ y]^2 & x [ y - z ]+2 y [ x + z ] & + z [ x - y ]=4[ y ]^2 aligned aligned & 3 x+ z =4 y & x + x + x + z 4 = y aligned y is the A M of x, x, x, x & z .