The possible values of p are p=11 or p=−4.
Let's solve the system of equations:
(5−p)^2 +(1−7)^2 =4(5−8)^2 +(1−2)^2 p=?
We can solve the system of equations by expanding the squares and then combining like terms.
Steps to solve:
1. Expand the squares:
(5−p)^2 +(1−7)^2
=4(5−8) +(1−2)^2 25−10p+p^2 +36=16+96+1 p^2 −10p+62 =113 p^2 −10p−51 =0
2. Factor the quadratic:
(p−11)(p+4)=0
3. Solve for p:
p=11 or p=−4
Answer:
p=11 or p=−4