The system of equations
$2 x^{2} - 3 y^{2} + z^{2} + 6 = 0,$
$x^{2} - 7 y^{2} - 2 z^{2} - 5 = 0$
and $5 x^{2} - y^{2} + 4 z^{2} + 23 = 0$ has

Unique real solution

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Finitely many real solutions

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Infinitely many solutions

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No real solution

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Solution

The correct option is D No real solution
$∵ Put x^{2} = t, y^{2} = u, z^{2} = v$

$\Rightarrow x^{2} = - 4, y^{2} = - 1, z^{2} = - 1$ the values of $x^{2}, y^{2} and z^{2}$ are negative.

$∴$ No real solution

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