Question:
If \[ a+b=7 \] and \[ ab=12 \] find:
\[ a^2+b^2 \]
Solution:
Using identity:
\[ (a+b)^2 = a^2+b^2+2ab \]
Substituting the given values:
\[ (7)^2 = a^2+b^2+2(12) \]
\[ 49 = a^2+b^2+24 \]
\[ a^2+b^2 = 49-24 \]
\[ =25 \]
If \[ a+b=7 \] and \[ ab=12 \] find:
\[ a^2+b^2 \]
Using identity:
\[ (a+b)^2 = a^2+b^2+2ab \]
Substituting the given values:
\[ (7)^2 = a^2+b^2+2(12) \]
\[ 49 = a^2+b^2+24 \]
\[ a^2+b^2 = 49-24 \]
\[ =25 \]