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Q.
If x, y, z are real and $4x^{2} + 9y^{2} + 16z^{2} - 6xy - 12yz - 8zx = 0,$ then x, y, z are in
Sequences and Series
Solution:
Multiplying the given expression by 2 and rewriting it, we have
$(2x-3y)^{2} +(3y -4z)^{2} +(4z -2x)^{2} =0$
$\Rightarrow 2x=3y=4z$
$\Rightarrow \frac{1}{x},\frac{1}{y},\frac{1}{z}$ are in A.P
$\Rightarrow x, y, x$ are in H.P.