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Monotonically Increasing Functions

If b - c x 2+...

Question

$I f (b - c) x^{2} + (c - a) x y + (a - b) y^{2}$ is a perfect square, then a, b, c are in

A

A.P

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B

G.P

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C

H.P

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D

none of these

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Solution

The correct option is A A.P
For a perfect square, the discriminant = 0
$∴ (c - a)^{2} - 4 (b - c) (A - b) = 0 \Rightarrow (c + a)^{2} - 4 b (c + a) + 4 b^{2} = 0 \Rightarrow (c + a - 2 b)^{2} = 0 \Rightarrow c + a = 2 b$

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Similar questions

(b - c) x^{2} + (c - a) x y + (a - b) y^{2} = 0

is a perfect square, then the quantities

a, b, c

a (b - c) x^{2} + b (c - a) x y + c (a - b) y^{2}

is a perfect square, then the quantities

a, b, c

a (b - c) x^{2} + b (c - a) x y + c (a - b) y^{2}

is a perfect square, then

a, b, c

Q. Assertion :If a, b, c are three positive real numbers such that

a + c \neq 0

\frac{1}{a} + \frac{1}{a - b} + \frac{1}{c} + \frac{1}{c - b} = 0

a, b, c

H . P

a, b, c

are distinct positive real numbers such that

a (b - c) x^{2} + b (c - a) x y + c (a - b) y^{2}

is a perfect square, then

a, b, c

H . P

.

If $b^{2}$ , $a^{2}$ , $c^{2}$ are in A.P., then a + b, b + c, c + a will be in

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