Factorize-x-2-2x-x-2-

Question Number 174036 by nadovic last updated on 23/Jul/22

Factorize x^{2} + \sqrt{2 x} + x + 2

Answered by dragan91 last updated on 23/Jul/22

x^{} = t^{2}

t^{4} + t \sqrt{2} + t^{2} + 2

t^{4} + 2 t \sqrt{2} - t \sqrt{2} + t^{2} + 2 =

t (t^{3} + {(\sqrt{2})}^{3}) + (t^{2} - t \sqrt{2} + 2) =

t (t + \sqrt{2}) (t^{2} - t \sqrt{2} + 2) + (t^{2} - t \sqrt{2} + 2) =

(t^{2} - t \sqrt{2} + 2) (t^{2} + t \sqrt{2} + 1)

(x - \sqrt{2 x} + 2) (x + \sqrt{2 x} + 1)

Commented by nadovic last updated on 23/Jul/22

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