MCQ
If $a,\,b,\,c$ are in $G.P.$, then
- A$a({b^2} + {a^2}) = c({b^2} + {c^2})$
- ✓$a({b^2} + {c^2}) = c({a^2} + {b^2})$
- C${a^2}(b + c) = {c^2}(a + b)$
- DNone of these
✓
Answer
Correct option: B.
$a({b^2} + {c^2}) = c({a^2} + {b^2})$
b
(b) If $a,\;b,\;c$ are in $G.P.$ Then ${b^2} = ac$
(b) If $a,\;b,\;c$ are in $G.P.$ Then ${b^2} = ac$
$ \Rightarrow $ ${b^2}(a - c) = ac(a - c)$
$ \Rightarrow $${b^2}a - {b^2}c = {a^2}c - a{c^2}$
$ \Rightarrow $ $a({b^2} + {c^2}) = c({a^2} + {b^2})$.
Trick : Put $a = 1,\;b = 2,\;c = 4$ and check the alternates.
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