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प्रश्न
उत्तर
`a/b = b/c ⇒ b^2 = ac` ...(1)
LHS = (a2 + b2) (b2 + c2)
= (a2 + ac) (ac + c2) ...[Using 1]
= a(a + c) × c(a + c)
= ac(a + c)2
= b2 (a + c)2 ...[Using 1]
= [b (a + c)]2
= (ab + bc)2
∴ LHS = RHS
∴ (a2 + b2) (b2 + c2 ) = (ab + bc)2
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