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Question
If (a + b + c) (a - b + c) = a2 + b2 + c2 show that a, b, c are in continued proportion.
Solution
`( a + b + c )( a - b + c ) = a^2 + b^2 + c^2`
⇒ `[(a + c) + b][(a + c) - b] = a^2 + b^2 + c^2`
⇒ `( a + c )^2 -b^2 = a^2 + b^2 + c^2` ...[(a + b)(a - b) = a2 - b2]
⇒ `a^2 + c^2 + 2ac - b^2 = a^2 + b^2 +c^2`
⇒ `2b^2 = 2ac`
⇒ `b^2 = ac`
Therefore, a, b, c are in continued proportion.
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