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X+y+z= 0. So x3+y3+z3=3xyz

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X+y+z= 0. So x3+y3+z3=3xyz

Posted by Vivek Anand 8 years, 6 months ago

CBSE > Class 09 > Mathematics

2 answers

Aryan Manglani 8 years, 6 months ago

Given,X+Y+Z=0 so, x3+y3+z3=3xyz so, By transposing the value z to the 0 so, it becomes x+y=0-z.so We have the value x+y=-z.equation 1 So, now In equation 1.Both sides cubing So,(x+y)3=(-z)3. We can now use the formula:X3+y3+3xyz= (-z)3.So,now we have the equation x3+y3+3xy(-z)=(-z).So,now we can write it as x3+y3-3xyz=(-z).So, by transposing both the terms with each other it becomes like this:x3+y3+z3=3xyz,because by transposing both the terms their signs will be changed.So, hence proved.ANS.

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Aman Verma 8 years, 6 months ago

X3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx)

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CBSE > Class 09 > Mathematics