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Determinants

Which one of following is correct if a, b and c are sides of a triangle ABC and \(\begin{vmatrix}a^2 & b^2 & c^2 \\(a + 1)^2 & (b + 1)^2 & (c + 1)^2 \\ (a – 1)^2 & (b – 1)^2 & (c – 1)^2 \end {vmatrix}\) ?


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What is the value of x if, \(\begin{vmatrix}x & 3 & 6 \\3 & 6 & x \\6 & x & 3 \end {vmatrix}\) = \(\begin{vmatrix}2 & x & 7 \\x & 7 & 2 \\7 & 2 & x \end {vmatrix}\) = \(\begin{vmatrix}4 & 5 & x \\5 & x & 4 \\x & 4 & 6 \end {vmatrix}\)?

Which one of following is correct if a, b and c are sides of a triangle ABC and \(\begin{vmatrix}a^2 & b^2 & c^2 \\(a + 1)^2 & (b + 1)^2 & (c + 1)^2 \\ (a – 1)^2 & (b – 1)^2 & (c – 1)^2 \end {vmatrix}\) ?

What is the value of k if \(\begin{vmatrix}y + z & x & x \\y & z + x & y \\z & z & x + y\end {vmatrix}\) ?

Which one of the following is correct if a

b and c are the sides of a triangle ABC and \(\begin{vmatrix}a^2 & b^2 & c^2 \\(a + 1)^2 & (b + 1)^2 & (c + 1)^2 \\ (a – 1)^2 & (b – 1)^2 & (c – 1)^2 \end {vmatrix}\) ?

Determinants

Objective-Mathematics