If a, b, c, d are in G.p., prove that : (i) (a2+b2),(b2+c2),(c2+d)2 ar

1.	If a, b, c, d are in G.p., prove that : (i) (a2+b2),(b2+c2),(c2+d)2 are in G.P. (ii) (a2−b2),(b2−c2),(c2−d)2 are in G.P. (iii) 1a2+b2,1b2+c2,1c2+d2 are in G.P. (iv) (a2+b2+c2),(ab+bc+cd),(b2+c2+d2)
Answer» If a, b, c, d are in G.p., prove that : (i) $(a^{2} + b^{2}), (b^{2} + c^{2}), (c^{2} + d)^{2}$ are in G.P. (ii) $(a^{2} - b^{2}), (b^{2} - c^{2}), (c^{2} - d)^{2}$ are in G.P. (iii) $\frac{1}{a^{2} + b^{2}}, \frac{1}{b^{2} + c^{2}}, \frac{1}{c^{2} + d^{2}}$ are in G.P. (iv) $(a^{2} + b^{2} + c^{2}), (a b + b c + c d), (b^{2} + c^{2} + d^{2})$

If a, b, c, d are in G.p., prove that : (i) (a2+b2),(b2+c2),(c2+d)2 are in G.P. (ii) (a2−b2),(b2−c2),(c2−d)2 are in G.P. (iii) 1a2+b2,1b2+c2,1c2+d2 are in G.P. (iv) (a2+b2+c2),(ab+bc+cd),(b2+c2+d2)

Answer»

If a, b, c, d are in G.p., prove that :

(i) $(a^{2} + b^{2}), (b^{2} + c^{2}), (c^{2} + d)^{2}$ are in G.P.

(ii) $(a^{2} - b^{2}), (b^{2} - c^{2}), (c^{2} - d)^{2}$ are in G.P.

(iii) $\frac{1}{a^{2} + b^{2}}, \frac{1}{b^{2} + c^{2}}, \frac{1}{c^{2} + d^{2}}$ are in G.P.

(iv) $(a^{2} + b^{2} + c^{2}), (a b + b c + c d), (b^{2} + c^{2} + d^{2})$