If a, b, c and d are in G.P show that (a2 + b2 + c2) (b2 + c2 + d… - Vidyadip

Question

If a, b, c and d are in G.P show that (a²+ b²+ c²) (b²+ c²+ d²) = (ab + bc + cd)².

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Answer

a, b, c, d are in G. P
b = ar
c = ar²
d = ar³
L. H. S = (a² + b² + c²) (b² + c² + d²)
= (a² + a²r² + a²r⁴) (a²r² + a²r⁴ + a²r⁶)
= a⁴r² (1 + r² + r⁴)²
R. H. S. = (ab + bc + cd)²
= (a²r + a²r³ + a²r⁵)²
= a⁴r² (1 + r² + r⁴)²
H.p

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