Question

if p^2+q^2+r^2=20 and pq+qr+rs=15, then value of p+q+r is?

Answer 1

We have an algebraic identity
(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)
We can use the above identity to solve the problem
(p+q+r)^2=p^2+q^2+r^2+2(pq+qr+rp)
(p+q+r)^2=20+2(15)=50
p+q+r=√50=7.07(approx)

Hope this answer helps you!!

Answer 2

p²+q²+r²= 20
pq+qr+rs=15
multiplay it with 2 we get
2pq+2qr+2rs=30

we have formula
(p+q+r)²= p²+q²+r²+2pq+2qr+2rs

putting values we get

(p+q+r)² = 20+30
(p+q+r)= √50

p+q+r= 5√2