Question

Factorise y^4+4y^2+3​

Answer 1

Step-by-step explanation:

$y {}^{4} + 4y {}^{2} + 3 \\ let \: y {}^{2} = t \\ t {}^{2} + 4t + 3 = 0 \\ t {}^{2} + 3t + t + 3 = 0 \\ t(t + 3) + 1(t + 3) = 0\\ (t + 3)(t + 1) = 0 \\ \\ t + 3 = 0 \\ t = - 3 \\ y {}^{2} = - 3 \\ y = \sqrt{ - 3} \\ \\ t + 1 = 0 \\ t = - 1 \\ y {}^{2} = - 1 \\ y = \sqrt{ - 1}$

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