Question

If p2+q2 +r2=82 and pq+qr+pr=18 ; find p+q+r

Please Solve It As Fast As Possible.​

Answer 1

Provided:-

• $p^2 + q^2 + r^2 = 8^2$
• $pq + qr + pr = 18$.

We know,

$(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$

⇒ $(p + q + r)^2 = p^2 + q^2 + r^2 + 2(pq + qr + pr)$

By putting the values:-

⇒ $p + q + r = \sqrt{8^2 + 2(18)}$

⇒ $p + q + r = \pm \sqrt{64 + 36}$

⇒ $p + q + r = \pm 10$

So, the required value is $\pm 10$.