2. Polynomials
hard

ઘન મેળવ્યા સિવાય $(x-y)^{3}+(y-z)^{3}+(z-x)^{3} $ ના અવયવો પાડો.

Option A
Option B
Option C
Option D

Solution

આપણે જાણીએ છીએ કે $x^{3}+y^{3}+z^{3}-3 x y z=(x+y+z)\left(x^{2}+y^{2}+z^{2}-x y-y z-z x\right)$

જો $x + y+ 7 = 0$ હોય, તો

$x^{3}+y^{3}+z^{3}-3 x y z=0$ અથવા

$x^{3}+y^{3}+z^{3}=3 x y z$

$(x-y)+(y-z)+(z-x)=0$

$\therefore(x-y)^{3}+(y-z)^{3}+(z-x)^{3}=3(x-y)(y-z)(z-x)$

Standard 9
Mathematics

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