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If the real numbers x, y, z are such that x^2 + 4y^2 +16z^2 = 48 and xy + 4yz + 2zx = 24, what is the value of x^2 + y^2 + z^2?

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If the real numbers x, y, z are such that x2 + 4y2 +16z2 = 48 and xy + 4yz + 2zx = 24, what is the value of x2 + y2 + z2?

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x2 + 4y2 + 16z2 = 48 ...(i)

xy + 4yz + 2zx = 24 ...(ii)

Multiply (ii) by 2 and subtract from (i)

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