Question

in triangle abc ad perpendicular to bc such that 2bd =3cd proove that 5ab2 =5ac2+bc2

Answer 1

2/3bd=cd

2/3bd=bc-bd

2/3bd+bd=bc

5/3bd=bc

bd=3/5bc

ab2=ad2+bd2

ab2=ad2+9/25bc2                            cd=2/5bc

ab2=ac2+(-4/25+9/25)bc2

5ab2=5ac2=bc2