Question

when a+b+c+3a^1/3 b^2/3 +3a^2/3 b^1/3 is divided by a^1/3+b^1/3+c^1/3 what s the remainder

Answer 1

Answer:

When a+b+c+3a^{1/3}b^{2/3}+3a^{2/3}b^{1/3} is divided by a^{1/3}+b^1/3+c^{1/3} what is the remainder?

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Let a=x3,b=y3,c=z3a=x3,b=y3,c=z3

P=x3+y3+z3+3(x2y+y2x)=x3+y3+z3+3xy(x+y)P=x3+y3+z3+3(x2y+y2x)=x3+y3+z3+3xy(x+y)

To get remainder set x+y+z=0⟹x+y=−zx+y+z=0⟹x+y=−z

P=x3+y3+z3−3xyzP=x3+y3+z3−3xyz

This is known to be 00whenx+y+z=0.x+y+z=0.

Remainder=0