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Question

2x³ +2y³ +2z³- 6xyz= (x+y+z) [(x-y)² +(y-z)² +(z-x)² ] hence evaluate 2(7)³ +(9)³ + 2(13)³ -6(7)(9)(13).

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Solution

2( 7 )³ + 2( 9)³ + 2( 13 )³ - 6 × 7 × 9 ×13

Suppose ,

7 = x , 9 = y and 13 = z

Now,

= 2x³ + 2y³ + 2z³ - 6xyz

Using identity :

= 2x³ +2y³ +2z³- 6xyz= (x+y+z) [(x-y)² +(y-z)² +(z-x)² ]

By putting the value of x,y and z.

= ( 7+9+13 ) { ( 7-9 )² + ( 9-13)² + ( 13-7 )² }


= ( 29 ) { ( -2 )² + ( -4 )² + ( 6 )² }

= 29 ( 4 + 16 + 36 )

= 29 × 56

= 1624



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