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If m/a=n/b ,let us show that (m2+n2)(a2+b2)=(am+bn)2​

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Answer:

firstly,

m/a = n/b then,,

mb = an

now,

from LHS

= (m² + n²) (a² + b²)

= m²a² + m²b² + à²n² + b²n²

= (ma)² + (mb)² + (an)² + (bn)²

= (ma)² + (an)² + (an)² + (bn)²

= (ma)² + 2(an)² + (bn)²

= (ma)² + 2(ma)(bn) + (bn)²

= (ma + bn)²

= RHS

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