Question:
If \[ a-b=5 \] and \[ ab=12 \] find:
\[ a^2+b^2 \]
Solution:
Using identity:
\[ (a-b)^2 = a^2+b^2-2ab \]
Substituting the given values:
\[ (5)^2 = a^2+b^2-2(12) \]
\[ 25 = a^2+b^2-24 \]
\[ a^2+b^2 = 25+24 \]
\[ =49 \]
If \[ a-b=5 \] and \[ ab=12 \] find:
\[ a^2+b^2 \]
Using identity:
\[ (a-b)^2 = a^2+b^2-2ab \]
Substituting the given values:
\[ (5)^2 = a^2+b^2-2(12) \]
\[ 25 = a^2+b^2-24 \]
\[ a^2+b^2 = 25+24 \]
\[ =49 \]