Using the properties of determinats, prove that |{:(((a+b)^(2))/(c),c,c),(a,((b+c)^(2))/(a),a),(b,b,((c+a)^(2))/(b)):}|=2(a+b+c)^(3). Or, If p ne0,qne0and|{:(p,q,palpha+q),(q,r,qalpha+r),(palpha+q,q alpha+r,0):}|=0 then using thepropetries of eterminants, prove that at least one of the following statements is true: (a) p,q,r are in GP(b) alpha is a root of the equation px^(2)+2qx+r=0.

Using the properties of determinats, prove that |{:(((a+b)^(2))/(c),c

1.	Using the properties of determinats, prove that \|{:(((a+b)^(2))/(c),c,c),(a,((b+c)^(2))/(a),a),(b,b,((c+a)^(2))/(b)):}\|=2(a+b+c)^(3). Or, If p ne0,qne0and\|{:(p,q,palpha+q),(q,r,qalpha+r),(palpha+q,q alpha+r,0):}\|=0 then using thepropetries of eterminants, prove that at least one of the following statements is true: (a) p,q,r are in GP(b) alpha is a root of the equation px^(2)+2qx+r=0.
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