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Question
Solve the following equations for the unknown:
(3x - 1)2 + (4x + 1)2 = (5x + 1)2 + 5
Solution
(3x - 1)2 + (4x + 1)2 = (5x + 1)2 + 5
Opening squares, we get
[9x2 + 1 + 2(3x)(1)] + [16x2 + 1 + 2(4x)(1)] = [25x2 + 1 2(5x)(1)] + 5
⇒ 25x2 + 2 + 8x + 6x
⇒ 25x2 + 6 + 10x
⇒ 4x = 4
⇒ x = 1
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