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  4. If area of triangle whose vertices are (a, a2),(b, b2),(c, c2) is 1 and area of another triangle whose vertices are (α2, α),(β2, β) and (γ2, γ) is 2 , then the absolute value of |(a+α)2 (b+α)2 (c+α)2 (a+β)2 (b+β)2 (c+β)2 (a+γ)2 (b+γ)2 (c+γ)2|is equal to

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Q. If area of triangle whose vertices are $\left(a, a^2\right),\left(b, b^2\right),\left(c, c^2\right)$ is 1 and area of another triangle whose vertices are $\left(\alpha^2, \alpha\right),\left(\beta^2, \beta\right)$ and $\left(\gamma^2, \gamma\right)$ is 2 , then the absolute value of $\begin{vmatrix}(a+\alpha)^2 & (b+\alpha)^2 & (c+\alpha)^2 \\ (a+\beta)^2 & (b+\beta)^2 & (c+\beta)^2 \\ (a+\gamma)^2 & (b+\gamma)^2 & (c+\gamma)^2\end{vmatrix}$is equal to

Determinants

Solution:

Given determinant $=\begin{vmatrix}a ^2 & 2 a & 1 \\ b ^2 & 2 b & 1 \\ c ^2 & 2 c & 1\end{vmatrix}\times\begin{vmatrix}1 & \alpha & \alpha^2 \\ 1 & \beta & \beta^2 \\ 1 & \gamma & \gamma^2\end{vmatrix}=2 \times 2 \times 1 \times 2 \times 2=16$