question_answer

If a + b = 25 and \[{{a}^{2}}+{{b}^{2}}=225,\]then find ab.

Answer:

We know that,

\[{{\left( a+b \right)}^{2\text{ }}}=\text{ }{{a}^{2}}+{{b}^{2}}+2ab~~\]

Here, \[a+b\text{ }=25,\text{ }{{a}^{2}}+{{b}^{2}}=225~~\]

\[\Rightarrow \]   \[{{(25)}^{2}}=225+2ab\]

\[\Rightarrow \]   625 = 225 + 2ab

\[625-225=2ab\]

\[\Rightarrow \,\] 400 = 2ab

\[\Rightarrow \,\] \[ab=\frac{400}{2}\]

\[\Rightarrow \,\]ab = 200