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Factor polynomialHello, When making some exercices to improve my general understanding of basic mathematics, I stumbled upon following problem: to factorise X^2 + ((sqrt 2)+(sqrt 3)) x + (sqrt 6) I do not recognise the form (a+b)^2, so I tried going for the discriminant, which would be ((sqrt 2)+(sqrt 3))^2 - 4*(sqrt 6) = 2 + 3 + 2((sqrt 2)+(sqrt 3)) - 4 (sqrt 6) = 5 - 2(sqrt6) I thus there are two roots to this polynomial, but I do not know how to calculate them. When trying to use the formula (-b +- (sqrt D))/2a, the numbers (especially the square roots) get to hard for me to work with. The book lists the solutions (x+ (sqrt 2)) * (x+ (sqrt 3)), but not how to get there. Could anyone give me a hint here please? |

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-Dan |

Oh, wow, I didn't know that equation. Thank you! |

Quote:
-Dan |

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$\displaystyle x^2 + ( \sqrt{3} + \sqrt{2} )x + \sqrt{6} = 0$ $\displaystyle x = \dfrac{-(\sqrt{3} + \sqrt{2} ) \pm \sqrt{ ( \sqrt{3} + \sqrt{2} )^2 - 4 (1) \sqrt{6} }}{2 (1)}$ $\displaystyle x = \dfrac{ - ( \sqrt{3} + \sqrt{2} ) \pm \sqrt{3 + 2 + 2\sqrt{6} - 4 \sqrt{6} } }{2}$ $\displaystyle x = \dfrac{ -( \sqrt{3} + \sqrt{2} ) \pm \sqrt{3 + 2 - 2 \sqrt{6} } }{2}$ $\displaystyle x = \dfrac{ -(\sqrt{3} + \sqrt{2} ) \pm \sqrt{(\sqrt{3} - \sqrt{2})^2}}{2}$ $\displaystyle x = \dfrac{ -(\sqrt{3} + \sqrt{2} ) \pm (\sqrt{3} - \sqrt{2} )}{2}$ I leave it to you to finish this. -Dan |

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