Question

If (a²+b²)(m²+n²)=(am+bn)², prove that a:m=b:n.

Answer 1

(a² + b²)(m² + n²) = (am + bn)²
=> a²(m² + n²) + b²(m² + n²) = a²m² + b²n² +2abmn
=> a²m² + a²n² + b²m² + b²n² = a²m² + b²n² +2abmn
=>a²n² + b²m² -2abmn = 0
=> (an)² + (bm)² -2(an)(bm)= 0
=>(an - bm)² =0
=> an - bm = 0
=> a: m = b:n
hence, proved

Answer 2

Answer:

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