Last updated at May 29, 2018 by Teachoo
Transcript
Ex 9.3,6 For what values of x, the numbers (โ2)/7, x, (โ7)/2 are in G.P? Since (โ2)/7, x, (โ7)/2 are in GP So common ratio will be same Common ratio (r) = (๐๐๐๐๐๐ ๐ก๐๐๐ )/(๐น๐๐๐ ๐ก ๐ก๐๐๐) = ๐ฅ/((โ2)/7) = 7๐ฅ/(โ2) Also, Common ratio (r) = (๐โ๐๐๐ ๐ก๐๐๐ )/(๐๐๐๐๐๐ ๐ก๐๐๐) = ((โ7)/2)/๐ฅ = (โ7)/2๐ฅ From (1) & (2) 7๐ฅ/(โ2) = (โ7)/2๐ฅ 7x ร 2x = (-7) ร (-2) 14x2 = 14 x2 = 14/14 x2 = 1 x = ยฑ โ1 x = ยฑ1 So, x = 1 or x = -1 GP is (โ2)/7, x, (โ7)/2 For x = 1, GP is (โ2)/7, 1, (โ7)/2 For x = โ1, GP is (โ2)/7, โ1, (โ7)/2 Hence possible numbers in GP are (โ2)/7, 1, (โ7)/2 or (โ2)/7, โ1, (โ7)/2
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