Question Number 132358 by Engr_Jidda last updated on 13/Feb/21
$${find}\:{the}\:{equation}\:{whose}\:{roots}\:{are} \\ $$$$\alpha\:{and}\:\beta.\:{find}\:\alpha\:{and}\:\beta\:{if}\:\:\alpha−\beta=\mathrm{2}\:{and}\:\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} =\mathrm{3} \\ $$
Commented by Dwaipayan Shikari last updated on 13/Feb/21
$${x}^{\mathrm{2}} −\left(\alpha+\beta\right){x}+\alpha\beta=\mathrm{0}\Rightarrow{x}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{2}}{x}+\frac{\mathrm{7}}{\mathrm{16}}=\mathrm{0} \\ $$$$\left(\alpha−\beta\right)\left(\alpha+\beta\right)=\mathrm{3}\Rightarrow\alpha+\beta=\frac{\mathrm{3}}{\mathrm{2}}\:\:\wedge\:\alpha−\beta=\mathrm{2} \\ $$$$\alpha=\frac{\mathrm{7}}{\mathrm{4}}\:\:\:\beta=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$
Commented by Engr_Jidda last updated on 13/Feb/21
$${thank}\:{you}\:{sir} \\ $$