Question

if a²(b+c),b²(c+a),c²(a+b) are in ap and a,b,c are not in ap.then the relation between a,b,c is given by​

Answer 1

Step-by-step explanation:

How can I prove that if “a^2 (b+c), b^2(c+a) and c^2 (a+b) are in AP then either a, b, c are in AP or ab+bc+ca=0” ?

Given: a2²b+c),b²(c+a),c²(a+b) are in AP

=> difference between second and first term = difference between third and second term

=>b²(c+a)−a²(b+c)=c²(a+b)−b²(c+a)

=>b²c+ab²−a²b−a²c=ac²+bc²−b²c−b²a

=>c(b²−ca²)+ab(b−a)=a(c²−b²)+bc(c−b)

=>c(b+a)(b−a)+ab(b−a)=a(c+a)(c−a)+bc(c−b)

=>(b−a)∗(ab+bc+ca)=(c−b)∗(ab+bc+ca)

The above expression holds good when:

• (ab+bc+ca) = 0

• If not, (b-a) = (c-b) => difference between b and a and the difference between c and b are same => a,b,c are in AP

Answer 2

Hello g how can I help u Leaving only maths

sorry