Equate the two expressions: x^{4} = 7x^{2} - 10

Rearrange: x^{4} - 7x^{2} + 10 = 0

Let z = x^{2}

z^{2} - 7z + 10 = 0

This factorises nicely as: (z - 2)(z - 5) = 0

So z = 2 and z = 5

or x^{2} = 2 and x^{2} = 5

n = 2^{1/2}, m = 5^{1/2} so m - n = 5^{1/2} - 2^{1/2}

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