Menu Close

Question-58618




Question Number 58618 by azizullah last updated on 26/Apr/19
Answered by mr W last updated on 26/Apr/19
roots: α,β  α+β=7  αβ=−9  (α−β)^2 =(α+β)^2 −4αβ=7^2 −4(−9)=85  ⇒∣α−β∣=(√(85)) =answer
$${roots}:\:\alpha,\beta \\ $$$$\alpha+\beta=\mathrm{7} \\ $$$$\alpha\beta=−\mathrm{9} \\ $$$$\left(\alpha−\beta\right)^{\mathrm{2}} =\left(\alpha+\beta\right)^{\mathrm{2}} −\mathrm{4}\alpha\beta=\mathrm{7}^{\mathrm{2}} −\mathrm{4}\left(−\mathrm{9}\right)=\mathrm{85} \\ $$$$\Rightarrow\mid\alpha−\beta\mid=\sqrt{\mathrm{85}}\:={answer} \\ $$
Commented by azizullah last updated on 27/Apr/19
Thank you sir!
$$\boldsymbol{\mathrm{Thank}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{sir}}! \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *