Question

Find r if p+q+r = 6 , p^2+q^2+r^2+2(pq-qr-pr) = 20

Answer 1

Answer:

r = 3 + √5

Step-by-step explanation:

let p+q = X

∴ p+q+r = X + r = 6   ...(1)

p² + q² + r² + 2(pq - qr - pr) = 20

∴ (p² + 2pq + q²) + r² - 2r(p+q) = 20

∴ (p + q)² + r² - 2r(p+q) = 20

... substituting p+q = X

∴ X² + r² - 2Xr = 20

∴ (r-X)² = 20

from eq 1... X+r = 6, i.e.  .. X = 6-r

∴ [r - (6-r)]² = 20

∴ (2r - 6)² = 20

∴ 2r - 6 = √20

∴ 2r = 2√5 + 6

∴ r = 3 + √5