Question

Find the solution set p, q for the equation (p-2) (q-1/2)=pq-5 and (p+2)(q-1/2)=pq-5​

Answer 1

Step-by-step explanation:

On expanding the equation, we get

$pq - \frac{p}{2} - 2q + 1 = pq - 5 \\ \\ = > - \frac{p}{2} - 2q = - 6.......equ. \: (1)$

Taking LCM on LHS,

$= > - \frac{p - 2(2q)}{2} = - 6 \\ \\ = > - p - 4q = - 12$

$= > - p = - 12 + 4q \\ \\ = > - 1(p) = - 1(12 - 4q)$

$= > p = 12 - 4q ......equ. \: (2)$

Substituting value of p in equ. (1)

$\frac{12 - 4q}{2} - 2q = - 6 \\ \\ = > 6 - 2q - 2q = - 6$

$= > - 4q = - 12 \\ \\ = > q = 3$

Substituting value of q in equ. (2), we get,

$p = 12 - 4(3) \\ \\ = > p = 12 - 12 \\ \\ = > p = 0$

Therefore,

$p = 0 \\ q = 3$

For the second you can follow the above steps and find p = 24 and q = 4

Mark as Brainliest....

Answer 2

Answer: Value of p is 10 and value of q is 1/2

Step-by-step explanation:

Simplifying first equation:

$(p-2) (q-\frac{1}{2} )=pq-5$

⇒ $pq - \frac{p}{2} - 2q + 1 = pq -5$

⇒ $6 = \frac{p}{2} + 2q$

⇒ $12 = p + 4q$      ...eq(1)

Simplifying second equation :

$(p+2)(q-\frac{1}{2} )=pq-5$

⇒ $pq - \frac{p}{2} + 2q - 1 = pq -5$

⇒ $4 = \frac{p}{2} - 2q$

⇒ $8 = p - 4q$       ...eq(2)

eq(1) + eq(2) :

20 = 2p

p = 10

Substituting value of p in eq(2) :

8 = 10 - 4q

4q = 2

q = 1/2

Value of p is 10 and value of q is 1/2

#SPJ3