question_answer

                               Find the value of \[x,\text{ 10000}x\text{ }={{\left( 9982 \right)}^{2}}-{{\left( 18 \right)}^{2}}\]

Answer:

R.H.S     \[={{\left( 9982 \right)}^{2}}-{{\left( 18 \right)}^{2}}\]

\[=\left( 9982+18 \right)\left( 9982-18 \right)~\]

\[[Since,\text{ }{{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right)]\]

\[=\left( 10000 \right)\times \left( 9964 \right)~\]

L.H.S \[=\left( 10000 \right)\text{ }\times \text{ }x\]

Comparing L.H.S. and R.H.S, we get

\[10000x\text{ }=\text{ }10000\times 9964\]

or x \[=\frac{10000\times 9964}{10000}=9964\]