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Coordinate Geometry
Question
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Show that if a + b is not zero, then the equation a(x - a) = 2ab - b(x - b) has a solution x = a + b.

Answer

a(x - a) = 2ab - b(x - b)
⇒ ax - a2 = 2ab - bx + b2
⇒ ax + bx = a2 + 2ab + b2
∴ x(a + b) = (a + b)2 | Using Identity I
∴    x = a + b
| Cancelling (a + b) from both sides as (a + b) ≠ 0
Hence the given equation has a solution x = a + b.

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