



Get live Maths 1-on-1 Classs - Class 6 to 12
Examples
Example 1 (ii)
Example 2
Example 3 Important
Example 4 Deleted for CBSE Board 2023 Exams
Example 5 Deleted for CBSE Board 2023 Exams
Example 6 Important Deleted for CBSE Board 2023 Exams
Example 7 Deleted for CBSE Board 2023 Exams
Example 8 Important
Example 9
Example 10 Important
Example 11
Example 12 Important
Example 13
Example 14 Important
Example 15 Important
Example 16
Example 17 Important
Example 18 Important
Example 19 Important Deleted for CBSE Board 2023 Exams
Example 20 Deleted for CBSE Board 2023 Exams
Example 21 Important
Example 22
Example 23 You are here
Example 24 Important
Examples
Last updated at March 16, 2023 by Teachoo
Example 23, If a, b, c, d and p are different real numbers such that (a2 + b2 + c2)p2 2(ab + bc + cd) p + (b2 + c2 + d2) 0, then show that a, b, c and d are in G.P. Introduction If x2 + y2 + z2 0 So, if x2 + y2 + z2 0, x2 + y2 + z2 = 0 i.e. x = 0, y = 0 , z = 0 Example 23, If a, b, c, d and p are different real numbers such that (a2 + b2 + c2)p2 2(ab + bc + cd) p + (b2 + c2 + d2) 0, then show that a, b, c and d are in G.P. We need to show a, b, c & d are in GP So, common ratio must be same we have to prove / = / = / It is given that (a2 + b2 + c2) p2 2 (ab + bc + cd) p + (b2 + c2 + d2) 0 Solving a2p2 + b2p2 + c2p2 2abp 2bcp 2cdp + b2 + c2 + d2 0 (ap)2 + b2 2abp + (bp)2 + c2 2bcp + (cp)2 + d2 2cdp 0 Example 23, If a, b, c, d and p are different real numbers such that (a2 + b2 + c2)p2 2(ab + bc + cd) p + (b2 + c2 + d2) 0, then show that a, b, c and d are in G.P. We need to show a, b, c & d are in GP So, common ratio must be same we have to prove / = / = / It is given that (a2 + b2 + c2) p2 2 (ab + bc + cd) p + (b2 + c2 + d2) 0 Solving a2p2 + b2p2 + c2p2 2abp 2bcp 2cdp + b2 + c2 + d2 0 (ap)2 + b2 2abp + (bp)2 + c2 2bcp + (cp)2 + d2 2cdp 0 Solving (ap b) = 0 ap = b / = p Solving (bp c) = 0 bp = c / = p Solving (cp d) = 0 cp = d / = p This implies that (b )/a = (c )/b = (d )/c = p Hence a, b, c and d are in G.P.