Question

Which one among the following is correct if x, y, z are eliminated from, (\(\frac{bx}{y+z}\) = a, \(\frac{cy}{z+x}\) = b, \(\frac{az}{x+y}\) = c)?

(a) a^2b + b^2c + c^2a + abc = 0

(b) a^2b – b^2c + c^2a + abc = 0

(c) a^2b + b^2c + c^2a + 2abc = 0

(d) a^2b – b^2c – c^2a – abc = 0

The question was asked in my homework.

Query is from Application of Determinants topic in section Determinants of Mathematics – Class 12

Answer 1

Correct answer is (a) a^2b + b^2c + c^2a + abc = 0

The best explanation: \(\frac{bx}{y+z}\) = a  bx – ay – az = 0

\(\frac{cy}{z+x}\) = b  bx – cy + bz = 0

\(\frac{az}{x+y}\) = c  cx + cy – az = 0  

\(\begin{vmatrix}b & -a & -a \\b & -c & b \\c & c & -a \end {vmatrix}\) = 0

Or, b(ca – bc) + a(-ab – bc) – a(bc + c^2) = 0

or, abc – b^2c – a^2b – abc – abc – ac^2 = 0

or, a^2b + b^2c + c^2a + abc = 0 which is the required eliminate.