Using properties of determinants, prove that ∣∣∣∣∣∣∣(a+b)2ccca(b+c)2aabb(c+a)2b∣∣∣∣∣∣∣=2(a+b+c)3 OR If p≠0,q≠0 and ∣∣∣∣pqpα+qqrpα+rpα+qqα+r0∣∣∣∣=0, then, using properties of determinants. Prove that at least one of the following statements is true: (a) p, q, r are in G.P. (b) α is a root of the equation px2+2qx+r=0

Using properties of determinants, prove that ∣∣∣∣∣∣∣(a+b

1.	Using properties of determinants, prove that ∣∣∣∣∣∣∣(a+b)2ccca(b+c)2aabb(c+a)2b∣∣∣∣∣∣∣=2(a+b+c)3 OR If p≠0,q≠0 and ∣∣∣∣pqpα+qqrpα+rpα+qqα+r0∣∣∣∣=0, then, using properties of determinants. Prove that at least one of the following statements is true: (a) p, q, r are in G.P. (b) α is a root of the equation px2+2qx+r=0
Answer» Using properties of determinants, prove that $∣ ∣∣∣∣∣ ∣ \begin{matrix} \frac{(a + b)^{2}}{c} & c & c a & \frac{(b + c)^{2}}{a} & a b & b & \frac{(c + a)^{2}}{b} \end{matrix} ∣ ∣∣∣∣∣ ∣ = 2 (a + b + c)^{3}$ OR If $p \neq 0, q \neq 0$ and $∣ ∣∣ ∣ \begin{matrix} p & q & p α + q q & r & p α + r p α + q & q α + r & 0 \end{matrix} ∣ ∣∣ ∣ = 0$ , then, using properties of determinants. Prove that at least one of the following statements is true: (a) p, q, r are in G.P. (b) $α$ is a root of the equation $p x^{2} + 2 q x + r = 0$