If(a − c)/a = (b − c)/b = c/(a + b) then each ratio equal to :(a) 1/2 (b) −1 (c) either 1/2 or −1 (d) neither 1/2 nor −1

Question

KnowledgeBoat · Accepted Answer

Given, From the first relation: a = k(b + c) ....(1) From the second relation: b = k(c + a) ....(2) From the third relation: c = k(a + b) ....(3) Adding (1), (2) and (3): a + b + c = k(b + c) + k(c + a) + k(a + b) a + b + c = k((b + c) + (c + a) + (a + b)) a + b + c = k(b + c + c + a + a + b) a + b + c = k(a + a + b + b + c + c) a + b + c = k(2a + 2b + 2c) a + b + c = 2k(a + b + c) If a + b + c 0, then, 2k = 1 If a + b + c = 0, then the equations will be, a + b = -c ....(4) b + c = -a ....(5) c + a = -b ....(6) Subtituting values in k = -1 Hence, Option 3 is the correct option.

Mathematics

If(a − c)/a = (b − c)/b = c/(a + b) then each ratio equal to :(a) 1/2 (b) −1 (c) either 1/2 or −1 (d) neither 1/2 nor −1

Ratio Proportion

Related Questions

If b is the mean proportion between a and c, then the mean proportion between (a² + b²) and (b² + c²) is:
a(b + c)
b(a + c)
c(a + b)
none of these

Mathematics

If(a − c)/a = (b − c)/b = c/(a + b) then each ratio equal to :(a) 1/2 (b) −1 (c) either 1/2 or −1 (d) neither 1/2 nor −1

Ratio Proportion

Related Questions

If b is the mean proportion between a and c, then the mean proportion between (a2 + b2) and (b2 + c2) is:a(b + c)b(a + c)c(a + b)none of these

If b is the mean proportion between a and c, then the mean proportion between (a² + b²) and (b² + c²) is:
a(b + c)
b(a + c)
c(a + b)
none of these