Question

α+β=5 and α2+β2=53 then αβ=?


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Answer 1

Step-by-step explanation:

Given:-

$\alpha+{\beta}=5$

${{\alpha}}^{2}+{{\beta}}^{2}=53$

To find:-

${\alpha}{\beta}$

Solution:-

$\alpha+{\beta}=5$

${:}\longrightarrow$$({{\alpha}+{\beta})}^{2}={5}^{2}$

${:}\longrightarrow$${{\alpha}^{2}+{\beta}^{2}}+2 {\alpha}{\beta}=25$

${:}\longrightarrow$$53+2 {\alpha}{\beta}=25$

${:}\longrightarrow$$2 {\alpha }{\beta}=25-53=-28$

${:}\longrightarrow$${\alpha}{\beta}={\frac {-28}{2}}$

${:}\longrightarrow$${\underline{\boxed{\bf {{\alpha}{\beta}=-14}}}}$