Question

Solve for p and q if
p+q=2(p-q)
pq=675​

Answer 1

Step-by-step explanation:-

Let p + q = 2( p - q) be eqn.1 and pq = 675 be eqn.2

Now , lets expand eqn.1

`=> p + q = 2p - 2q`

`=> 2p - p = 2q + q`

`=> p = 3q`

Lets put the value of p in eqn.2

`=> 3q * q = 675`

`=> 3q^(2) = 675`

`=> q^(2) = (675)/(3) = 225`

`=> q = √(225) = +15 \: or \: -15`

Lets find out the value of p.

When q = +15 ,
`p = 3 * 15 = 45`

When q = -15 ,
`p = 3 * - 15 = -45`

Hence ,

p = ±45

q = ±15

Answer 2

q=15

p=45

Explanation:

p+q=2(p-q)

p+q=2p-2q

simplify: add 2q to each side and subtract one p from each side of the equation.

p=3q

given that pq=675, substitute:

(3q)q=675

3q^2=675

q^2=225

q=15

then p=3q or p=3(15)=45

p=45