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Step-by-step explanation:
In Δ ABL,
BL² = AB² + AL²
BL² = AB² + AC/2² ( Since L is median )
4 BL² = 4 AB² + AC² ( By taking LCM and taking the 4 LHS )........I
In Δ CMA
CM² = AM² + AC²
CM² = AC²+ AB/2²
4 CM² = 4 AC² + AB²............II
By adding I AND II
4 ( CM² + BL²) = 4 AC² + AC² + AB²+4AB²
4 ( CM² + BL²) = 5 ( AC² + AB² )
4 ( CM² + BL²) = 5 BC² ( AC² + AB² = BC² )
Hence Proved
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