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