Question

if a-2b-3c+4d/a+2b-3c-4d = a-2b+3c-4d/a+2b+3c+4d,show that 2ad=3bc​

Answer 1

Step-by-step explanation:

$\frac{a - 2b - 3c + 4d}{a + 2b - 3c - 4d} = \frac{a - 2b + 3c - 4d}{a + 2b + 3c + 4d} \\ by \: cross \: multiplication \\ a - 2b - 3c + 4d(a + 2b + 3c + 4d) = a + 2b - 3c - 4d(a - 2b + 3c - 4d)$

${a}^{2} + 2ab + 3ac + 4ad - 2ab - 4 {b}^{2} - 6bc - 8bd - 3ac - 6bc - 9 {c}^{2} - 12cd + 4ad + 8bd + 12cd + 16 {d}^{2} = {a}^{2} + 2ab - 3ac - 4ad - 2ab - 4 {b}^{2} + 6bc + 8bd + 3ac + 6bc - 9 {c}^{2} - 12cd - 4ad - 8bd + 12cd + 16 {d}^{2} \\ 4ad - 6bc - 6bc + 4ad = - 4ad + 6bc + 6bc - 4ad \\ 8ad - 12bc = 12bc - 8ad \\ 8ad + 8ad = 12bd + 12bd \\ 16ad = 24bd \\ 8(2ad) = 8(3bd) \\ 2ad = \frac{8(3bd)}{8} \\ 2ad = 3bd$

so the statement is proved