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`|{:(" "x," "c+x," "b+x),(" "c+x," "x," "a+x),(" "b+x," "a+x," "x):}|=0`

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The correct Answer is:
`(2abc)/(a^2+b^2+c^2-2(ab+bc+ca)`
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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. |{:(x+1," "2," "3),(" "1,x+1," "3),(" "3,-6,x+1):}|=0

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  2. |{:(a-x," "b," "c),(" "b,c-x," "a),(" "c," "a,b-x):}|=0

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  3. |{:(" "x," "c+x," "b+x),(" "c+x," "x," "a+x),(" "b+x," "a+x," ...

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  4. |{:(2-x," "2," "3),(" "2,5-x," "6),(" "3," "4,10-x):}|=0

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  5. solve:|{:(3+x,3-x,3-x),(3-x,3+x,3-x),(3-x,3-x,3+x):}|=0

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  6. |{:(x-2,2x-3,3x-4),(x-4,2x-9,3x-16),(x-8,2x-27,3x-64):}|=0

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  7. |{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}|=0[where" "a neb nec]

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  8. Solve: |{:(3,5,x),(7,x,7),(x,5,3):}|=0

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  9. |{:(x+a," "b," "c),(" "a,x+b," "c),(" "a," "b,x+c):}|=0

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  10. |{:(3x-8," "3," "3),(" "3,3x-8," "3),(" "3," "3,3x-8):}|=0

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  11. |{:(15-2x,11-3x,7-x),(11,17,14),(10,16,13):}|=0

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  12. |{:(" "1," "1," "x),(p+3,p+1,p+x),(" "3,x+1,x+1):}|=0

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  13. If x and y are real and x +iy=|{:(6i,-3i,1),(4,3i,-1),(20,3,i):}|=0 , ...

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  14. solve : |{:(x-2,2,5),(x-7,3,6),(2x-6,4,7):}|=0

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  15. solve |{:(x-2," "3," "3),(" "3,x+4," "5),(" "3," "5,x+4):}|=0

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  16. show that x =2 is a root to the equation |{:(x,-6,-1),(2,-3x,x-3),(-...

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  17. |{:(" "1+a^2-b^2," "2ab," "-2b),(" "2ab,1-a^2+b^2," ...

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  18. |{:((b+c)^2," "a^2," "a^2),(" "b^2,(c+a)^2," "b^2),(" "c^2," "c^2,(...

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  19. Factorise : |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|

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  20. |{:(b+c,a,b),(c+a,c,a),(a+b,b,c):}|

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