If a, b, c, d are in G.P., prove that : (i) ab−cdb2−c2=a+cb (ii) (

1.	If a, b, c, d are in G.P., prove that : (i) ab−cdb2−c2=a+cb (ii) (a+b+c+d)2=(a+b)2+2(b+c)2+(c+d)2 (iii) (b+c)(b+d)=(c+d)(c+d)
Answer» If a, b, c, d are in G.P., prove that : (i) $\frac{a b - c d}{b^{2} - c^{2}} = \frac{a + c}{b}$ (ii) $(a + b + c + d)^{2} = (a + b)^{2} + 2 (b + c)^{2} + (c + d)^{2}$ (iii) $(b + c) (b + d) = (c + d) (c + d)$

If a, b, c, d are in G.P., prove that : (i) ab−cdb2−c2=a+cb (ii) (a+b+c+d)2=(a+b)2+2(b+c)2+(c+d)2 (iii) (b+c)(b+d)=(c+d)(c+d)

Answer»

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

(i) $\frac{a b - c d}{b^{2} - c^{2}} = \frac{a + c}{b}$

(ii) $(a + b + c + d)^{2} = (a + b)^{2} + 2 (b + c)^{2} + (c + d)^{2}$

(iii) $(b + c) (b + d) = (c + d) (c + d)$