solve the following mathematical problems:

if $\frac{a}{q - r} = \frac{b}{r - p} = \frac{c}{p - q}$ then show that, a+b+c=pa+qb+rc

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

$L e t, \frac{a}{q - r} = \frac{b}{r - p} = \frac{c}{p - q} = k s o, \frac{a}{q - r} = k a = k (q - r); b = k (r - p); c = k (p - q) L . H . S . = a + b + c = k (q - r) + k (r - p) + k (p - q) = k (q - r + r - p + p - q) = k \times 0 = 0 R . H . S = p a + q b + r c = p [k (q - r)] + q [k (r - p)] + r [k (p - q)] = p (k q - k r) + q (k r - k p) + r (k p - k q) = p k q - p k r + q k r - p k q + p k r - q k r = 0$