Question

if a^2-b^2=19 find the value of a^2+ab+b^2​

Answer 1

${a}^{2} - {b}^{2} = 19 \\ \\ (a \: + b) \: (a - b) = 19 \\ \\ (a + b) = \frac{19}{a - b} \\ \\ squaring \: both \: side \\ \\ {(a + b)}^{2} = \frac{ {19}^{2} }{ {(a - b)}^{2} } \\ \\ {a}^{2} + {b}^{2} + 2ab = \frac{361}{ {(a - b)}^{2} }$

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