If p+q+r=9 and pq+qr+pr=26 then p2+q2+r2 =
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Given that p+q+r=9
pq+qr+pr=26
p2+q2+r2=?
squaring on both sides
(p+q+r)2=(9)2
p2+q2+r2+2pq+2qr+2rp=8
p2+q2+r2+2(pq+qr+rp)=81
p2+q2+r2+2(26)=81. (pq+qr+rq=26)
p2+q2+r2+52=81
p2+q2+r2=81-52
therefore, p2+q2+r2=29
pq+qr+pr=26
p2+q2+r2=?
squaring on both sides
(p+q+r)2=(9)2
p2+q2+r2+2pq+2qr+2rp=8
p2+q2+r2+2(pq+qr+rp)=81
p2+q2+r2+2(26)=81. (pq+qr+rq=26)
p2+q2+r2+52=81
p2+q2+r2=81-52
therefore, p2+q2+r2=29
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