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Home » If (p2 + q2), (pq + qr), (q2 + r2) are in GP then prove that p, q, r are in GP
If (p2 + q2), (pq + qr), (q2 + r2) are in GP then prove that p, q, r are in GP
CBSE | Class 11 | Excercise 12E | Geometrical Progression | Maths | RS Aggarwal
If (p2 + q2), (pq + qr), (q2 + r2) are in GP then prove that p, q, r are in GP

Answer : To prove: p, q, r are in GP

Given: (p2 + q2), (pq + qr), (q2 + r2) are in GP Formula used: When a,b,c are in GP, b2 = ac Proof: When (p2 + q2), (pq + qr), (q2 + r2) are in GP, (pq + qr)2 = (p2 + q2) (q2 + r2)

p2q2 + 2pq2r + q2r2 = p2q2 + p2r2 + q4 + q2r2 2pq2r = p2r2 + q4

pq2r + pq2r = p2r2 + q4 pq2r – q4 = p2r2 – pq2r q2(pr – q2) = pr (pr – q2) q2 = pr

From the above equation we can say that p, q and r are in G.P.

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