Find the Values of a and b if (a, −2) and (4, b²) ∈ R
Question
Let
\[ R=\{(x,y): x,y\in Z,\ y=2x-4\} \]
If
\[ (a,-2)\in R \]
and
\[ (4,b^2)\in R, \]
then write the values of \( a \) and \( b \).
Solution
Since
\[ (a,-2)\in R, \]
therefore,
\[ -2=2a-4 \]
\[ 2a=2 \]
\[ a=1 \]
Also,
\[ (4,b^2)\in R \]
Therefore,
\[ b^2=2(4)-4 \]
\[ b^2=4 \]
\[ b=\pm2 \]
Hence,
\[ \boxed{a=1,\ b=\pm2} \]