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a-b-9-ab-20-a-b-




Question Number 110728 by Study last updated on 30/Aug/20
a+b=9  ,  ab=20     a−b=?
$${a}+{b}=\mathrm{9}\:\:,\:\:{ab}=\mathrm{20}\:\:\:\:\:{a}−{b}=? \\ $$
Answered by som(math1967) last updated on 30/Aug/20
(a−b)^2 =(a+b)^2 −4ab  (a−b)^2 =81−80  ⇒(a−b)=±1
$$\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} =\left(\mathrm{a}+\mathrm{b}\right)^{\mathrm{2}} −\mathrm{4ab} \\ $$$$\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} =\mathrm{81}−\mathrm{80} \\ $$$$\Rightarrow\left(\mathrm{a}−\mathrm{b}\right)=\pm\mathrm{1} \\ $$

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