Question

Integers p,q,r satisfy p+q-r = 1 and
p^2 + q^2 - r^2 = -1 . What is the sum of all possible values of p,q,r

Answer 1

Answer:

p + q – r = 1

⇒ p + q = 1 + r

⇒ p ^2+q^2-r^2+2pq= 1+2r

-1+2pq=1+2r [ p^2+q^2-r^2=-1]

⇒ –1 + 2pq = 1 + 2r

⇒ 2pq = 2(1 + r)

⇒ pq = p + q

⇒ pq – p – q + 1 = 1

⇒ (p – 1) (q – 1) = 1

p = 2, q = 2

∴ p – 1 = 1 or q – 1 = 1 and p – 1 = –1 or q – 1 = –1

⇒ p = 2, q = 2 and p = 0 or q = 0, r = 3 and r = –1

Step-by-step explanation:

Hey Mate

Here's your answer

Please Mark me Brainliest