Question

if a,b,c,d are in g.p. prove that (b+c)(b+d)=(c+a)(c+d).​

Answer 1

Answer:

(b-c)² + (c-a)² + (d-b)²

=(ar-ar²)² + (ar²-a)² + (ar³-ar)²

=a²(r-r²)² + a²(r²-1)² + a²(r³-r)²

=a²[(r-r²)² + (r²-1)² + (r³-r)²}

=a^2[r^2+r^4-2r^3+r^4+1-2r^2+r^6+r^2-2r^4] \\\\=a^2[r^6+1-2r^3] \\\\=a^2(1-r^3)^2\\\\ =[a(1-r^3)]^2\\\\