Question

if a, b, c are in continued proportion -
prove that - a^2 + ab + b^2 / b^2 +bc + c^2 = a/c​

Answer 1

Answer:

If A, B, and C Are in Continued Proportion, Prove that (A^2 + Ab + B^2)/(B^2 + Bc + C^2) = A/C - Mathematics.

Answer 2

According to the question....

a:b::b:c

=> a×c = b×b

=> a/b = b/c

let's say a/b = b/c = x

=> a = bx and b= cx

=> a = cx² (because b=cx)

a²+ab+b²

b²+bc+c²

putting the value of a and b.....

c²x⁴ + c²x³ + c²x²

c²x² + c²x + c²

=> c²(x⁴ + x³ + x²)

c²( x²+x+1)

=> x⁴ + x³ + x²

x² + x + 1

=> x² ( x² + x + 1 )

x² + x + 1

= x²

a/c = cx²/c

=> a/c = x²

LHS = RHS

hence proved.....

and say thank you