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using the properties of determinants , solve the following for x :
 
 
| X+2   X+6   X-1   |
|                          |
| X+6   X-1   X+2   |   = 0
|                          |
| X-1   X+2   X+6   |

Asked by shivamthetrisal 21st March 2015, 6:53 PM
Answered by Expert
Answer:
C o n s i d e r space t h e space g i v e n space e q u a t i o n colon open vertical bar table row cell x plus 2 end cell cell x plus 6 end cell cell x minus 1 end cell row cell x plus 6 end cell cell x minus 1 end cell cell x plus 2 end cell row cell x minus 1 end cell cell x plus 2 end cell cell x plus 6 end cell end table close vertical bar equals 0 A p p l y i n g space R subscript 2 rightwards arrow R subscript 2 minus R subscript 3 space a n d space R subscript 3 rightwards arrow R subscript 3 minus R subscript 1 open vertical bar table row cell x plus 2 end cell cell x plus 6 end cell cell x minus 1 end cell row cell x plus 6 minus x plus 1 end cell cell x minus 1 minus x minus 2 end cell cell x plus 2 minus x minus 6 end cell row cell x minus 1 minus x minus 2 end cell cell x plus 2 minus x minus 6 end cell cell x plus 6 minus x plus 1 end cell end table close vertical bar equals 0 rightwards double arrow open vertical bar table row cell x plus 2 end cell cell x plus 6 end cell cell x minus 1 end cell row 7 cell negative 3 end cell cell negative 4 end cell row cell negative 3 end cell cell negative 4 end cell 7 end table close vertical bar equals 0 rightwards double arrow open parentheses x plus 2 close parentheses open parentheses negative 21 minus 16 close parentheses minus open parentheses x plus 6 close parentheses open parentheses 49 minus 12 close parentheses plus open parentheses x minus 1 close parentheses open parentheses negative 28 minus 9 close parentheses equals 0 rightwards double arrow open parentheses x plus 2 close parentheses open parentheses negative 37 close parentheses minus open parentheses x plus 6 close parentheses open parentheses 37 close parentheses plus open parentheses x minus 1 close parentheses open parentheses negative 37 close parentheses equals 0 rightwards double arrow x plus 2 plus x plus 6 plus x minus 1 equals 0 rightwards double arrow 3 x plus 7 equals 0 rightwards double arrow x equals fraction numerator negative 7 over denominator 3 end fraction
Answered by Expert 23rd March 2015, 11:06 AM
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