Question

Solve: `|(7,4,11),(-3,5,x),(-x,3,1)|` = 0

Answer 1

`|(7,4,11),(-3,5,x),(-x,3,1)|` = 0

∴ `7 |(5,x),(3,1)| - 4|(-3,x),(-x,1)| + 11|(-3,5),(-x,3)|` = 0

7(5 – 3x) – 4(-3 + x²) + 11(-9 + 5x) = 0

35 – 21x + 12 – 4x² – 99 + 55x = 0

- 4x² – 21x + 55x + 35 + 12 – 99 = 0

- 4x² + 34x – 52 = 0

2 × 26 = 52
-13	- 4
`(- 13)/2`	`(-4)/2`

Divide throughout by -2 we get

2x² – 17x + 26 = 0

(2x – 13) (x – 2) = 0

2x – 13 = 0  (or)   x – 2 = 0

x = `13/2`   (or)  x = 2

∴ x = `13/2`, x = 2