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Question
If `a/b = b/c` and `a , b , c > 0` then show that, (a + b + c) (b - c) = ab - c2
Solution
LHS = `a/b = b/c ⇒ b^2 = ac` ...(1)
`( a + b + c)( b - c )`
RHS = `ab - ac + b^2 - bc + bc - c^2`
= `ab - ac + ac - c^2` ...(From 1)
= `ab - c^2`
∴ LHS = RHS
∴ (a + b + c) (b - c) = ab - c2
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