If a^2+16 b^2+49 c^2-4 ab-7 ac-28 bc=0 then a, b, c are in (a) AP (b) GP (c) HP (d) None of the

step 1 I haven't given you another equation we'll just find out ABC are in what AP G G Ph B HB what seq

If a^2+16 b^2+49 c^2-4 ab-7 ac-28 bc=0 then a, b, c are in...

If $\mathrm{a}^{2}+16 \mathrm{~b}^{2}+49 \mathrm{c}^{2}-4 \mathrm{ab}-7 \mathrm{ac}-28 \mathrm{bc}=0$ then $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in
(a) AP
(b) $\mathrm{GP}$
(c) HP
(d) None of these

Key Concepts

Discriminant Analysis in Parametric Equations

When an expression in multiple variables is viewed as a quadratic in one variable, the discriminant becomes a powerful tool. A zero discriminant ensures that the quadratic has a unique solution, which in turn imposes specific relationships among the remaining variables.

Quadratic Forms and Factorization

Quadratic forms in several variables can be reorganized or factored to reveal hidden relationships among the variables. Recognizing a quadratic expression as a perfect square or as factorable into simpler components helps in reducing the problem to conditions that the variables must satisfy.

Understanding Progressions (AP, GP, HP)

A firm grasp of arithmetic, geometric, and harmonic progressions is crucial. In these sequences, the terms satisfy different conditions—such as differences, ratios, or reciprocal relations—and identifying which condition matches the derived relationship helps determine the specific progression that the variables form.

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