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Relations — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsRelations1 Mark
Question
Let $\text{R}=\{(\text{x, y}):\text{x, y}\in\text{Z},\text{y}=2\text{x}-4\}.$ If (a, -2) and $(4,\text{b}^2)\in\text{R},$ then write the values of a and b.
✓

Answer

We have,
$\text{R}=\{(\text{x, y}):\text{x, y}\in\text{Z},\text{y}=2\text{x}-4\}$
Now,
$y = 2x - 4$
Putting $y = -2$ and $x = a$, we get
$-2 = 2a - 4$
$\Rightarrow 4 - 2 = 2a$
$\Rightarrow 2 = 2a$
$\Rightarrow 2a = 2$
$\Rightarrow\text{a}=\frac{2}{2}=1$
Putting $y = b^2$​​​​​​​ and $x = 4$, we get
$b^2= 2 \times 4 - 4$
$\Rightarrow b^2 = 8 - 4$
$\Rightarrow b^2 = 4$
$\Rightarrow\text{b}=\pm2$
Hence, $\text{a}=1,\text{b}=\pm2$

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