Let R - x - y - x - y - Z - y -2 x -4- If a -2 and -4- b 2 - R- then write the values of a and b-

We have, R = (x, y) : x, y ϵ Z, y = 2x 4 Now, y = 2x 4 Putting y = 2 and x = a, we get 2 = 2a 4 ⇒ 4 2 = 2a ⇒ 2 = 2a ⇒ 2a = 2 ⇒ a = 2/2 = 1 Putting y ...

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Standard XII

Mathematics

Domain

Let R = x , y...

Question

Let $R = {(x, y) : x, y ϵ Z, y = 2 x - 4}$ . If (a, -2) and $4, b^{2}) ϵ R,$ then write the values of a and b.

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Solution

We have,

R = { $(x, y) : x, y ϵ Z, y = 2 x - 4$ }

Now,

y = 2x - 4

Putting y = - 2 and x = a, we get

-2 = 2a - 4

$\Rightarrow 4 - 2 = 2 a$

$\Rightarrow 2 = 2 a$

$\Rightarrow 2 a = 2$

$\Rightarrow a = \frac{2}{2} = 1$

Putting $y = b^{2}$ and x = 4, we get

$b^{2} = 2 \times 4 - 4$

$\Rightarrow b^{2} = 8 - 4$

$\Rightarrow b^{2} = 4$

$\Rightarrow b = \pm 2$

Hence, $a = 1, b = \pm 2.$

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Let R={(x,y):x,yϵZ,y=2x−4}. If (a, -2) and 4,b2)ϵR, then write the values of a and b.

We have, R = {(x,y):x,yϵZ,y=2x−4} Now, y = 2x - 4 Putting y = - 2 and x = a, we get -2 = 2a - 4 ⇒4−2=2a ⇒2=2a ⇒2a=2 ⇒a=22=1 Putting y=b2 and x = 4, we get b2=2×4−4 ⇒b2=8−4 ⇒b2=4 ⇒b=±2 Hence, a=1,b=±2.

Let $R = {(x, y) : x, y ϵ Z, y = 2 x - 4}$ . If (a, -2) and $4, b^{2}) ϵ R,$ then write the values of a and b.