Question

यदि a+b+c=0 , तो सिध्द करे कि a^2/bc+b^2/ca+c^2/ab=3​

Answer 1

Answer:

( a^2 ) / bc + ( b^2 ) / ac + ( c^2 ) / ab = 3

Step-by-step explanation:

Given,

a + b + c = 0

= > a + b = - c

Cubing on both sides :

= > ( a + b )^3 = ( - c )^3

= > a^3 + b^3 + 3ab( a + b ) = - c^3 { using ( x + y )^3 = x^3 + y^3 + 3xy( x + y ) }

= > a^3 + b^3 + 3ab( - c ) = - c^3 { from above, a + b = - c }

= > a^3 + b^3 - 3abc = - c^3

= > a^3 + b^3 + c^3 = 3abc

= > ( a^3 + b^3 + c^3 ) / abc = 3:

= > ( a^3 ) / abc + ( b^3 ) / abc + ( c^3 ) / abc = 3

= > ( a^2 ) / bc + ( b^2 ) / ac + ( c^2 ) / ab = 3

Hence proved.

Answer 2

Answer:

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