Suppose that a,b,c are distinct numbers such that (c−b)2−4(c−a)(a−b)=0, find the value of c−aa−b.
Answer:
1
- Given, (c−b)2−4(c−a)(a−b)=0, we need to find the value of c−aa−b.
- (c−b)2−4(c−a)(a−b)=0⟹(c−a+a−b)2−4(c−a)(a−b)=0⟹((c−a)+(a−b))2−4(c−a)(a−b)=0⟹(c−a)2+(a−b)2+2(c−a)(a−b)−4(c−a)(a−b)=0⟹(c−a)2+(a−b)2−2(c−a)(a−b)=0⟹((c−a)−(a−b))2=0⟹(c−a)−(a−b)=0⟹(c−a)=(a−b)⟹c−aa−b=1