Question

If (p² + q²), (pq + qr), (q² + r² ) are in GP then prove that p, q, r are in GP

Answer 1

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 + p² r² + q⁴ + q² r² 

2pq² r = p² r² + q⁴ 

pq² r + pq² r = p² r ² + q⁴ 

pq² r - q ⁴ = p² r ² - pq² r 

q ²(pr – q²) = pr (pr – q²) 

q² = pr 

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