Question

जर a(y + z) = b(z + x) = c(x + y) आणि a, b, c पैकी कोणत्याही दोन संख्या समान नाहीत तर `(y − z)/[a (b − c)] = (z − x)/[b (c − a)] = (x − y)/[c( a − b)]` हे दाखवा.

Answer 1

`a(y + z) = b(z + x) = c(x + y) = k`

∴ `(a(y + z))/(abc) = (b(z + x))/(abc) = (c(x+ y))/(abc)`

`(y + z)/(bc) =(z + x)/(ac) = (x+ y)/(ab)` = k

`k = ((x + y) - (z + x))/(ab - ac) = (y - z)/(a(b - c))`    ...(1)

`k = ((y + z) - (x + y))/(bc - ab) = (z - x)/(b(c - a))`     ...(2)

`k = ((z + x) - (y + z))/(ac - bc)  = (x - y)/(c(a - b))`    ...(3)

∴ `(a/b = c/d = k = (a - c)/ (b - d))`

∴ `(y - z) /(a(b - c)) = (z - x) /(b(c - a)) = (x - y) /(c(a - b))`