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b-b-3-0-b-gt-0-find-2b-2-14b-28-




Question Number 190039 by Shrinava last updated on 26/Mar/23
b+(√b)−3=0  b>0  find   2b^2 −14b + 28 = ?
$$\mathrm{b}+\sqrt{\mathrm{b}}−\mathrm{3}=\mathrm{0} \\ $$$$\mathrm{b}>\mathrm{0} \\ $$$$\mathrm{find}\:\:\:\mathrm{2b}^{\mathrm{2}} −\mathrm{14b}\:+\:\mathrm{28}\:=\:? \\ $$
Answered by cortano12 last updated on 26/Mar/23
 (√b) = 3−b⇒b=9−6b+b^2   ⇒b^2 −7b+9=0  ⇒2b^2 −14b+18=0  ⇒2b^2 −14b+28=10
$$\:\sqrt{\mathrm{b}}\:=\:\mathrm{3}−\mathrm{b}\Rightarrow\mathrm{b}=\mathrm{9}−\mathrm{6b}+\mathrm{b}^{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{b}^{\mathrm{2}} −\mathrm{7b}+\mathrm{9}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{2b}^{\mathrm{2}} −\mathrm{14b}+\mathrm{18}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{2b}^{\mathrm{2}} −\mathrm{14b}+\mathrm{28}=\mathrm{10} \\ $$

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