Prove that 4a2 – b2 + c2 + 4ac = 0.

If 2a – b + c = 0, prove that 4a² – b² + c² + 4ac = 0.

Answer :

It is given that

2a – b + c = 0

2a + c = b

By squaring on both sides

(2a + c)² = b²

Expanding using formula

(2a)² + 2 × 2a × c + c² = b²

By further calculation

4a² + 4ac + c² = b²

So we get

4a² – b² + c² + 4ac = 0

Hence, it is proved.

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