Question

If (a^2+b^2)(m^2+n^2) = (am+bn)^2, prove that a:m=b:n

Answer 1

Hi ,

LHS = ( a² + b² )( m² + n² )

= a² (m² + n² ) + b² ( m² + n² )

= a² m² + a² n² + b² m² + b² n²


RHS = ( am + bn )²

= a²m² + 2abmn + b² n²

LHS = RHS ( given )

a² n² + b² m² = 2abmn

a² n² + b² m² - 2an × bm = 0

( an - bm )² = 0

an - bm = 0

an = bm

a/m = b / n

Hence proved .

I hope this helps you.

: )