16. If a, b, c are in GP. And a^x = b^y=c^z=then prove that 1/x+1/z =2

1.	16. If a, b, c are in GP. And a^x = b^y=c^z=then prove that 1/x+1/z =2/y.
Answer» ANSWER: a^x = b^x = c² a, b, c→ GP b² = ac xloga = ylogb = zlogc xloga = y/2 logc xloga = y/2 (LOGA + LOGE) = 2 (2x - y)loga = ylogc loga/logc = y/2x-y (1) y/2 logac = zlogc y/2 (loga+logc) = zlogc yloga = (2z - y)logc loga/logc = 2z-y/y (2) (1) = (2) y/2x-y = 2z-y/y y² = (2x - y) (2z - y) 4 x z-y (2x + 2z) = 0 2 x 2 − y(x+2) = 0 2/y = 1/z + 1/x Step-by-step explanation: anhenseyo sweetums unnie, good morning.

16. If a, b, c are in GP. And a^x = b^y=c^z=then prove that 1/x+1/z =2/y.

Answer»

a^x = b^x = c²

a, b, c→ GP

b² = ac

xloga = ylogb = zlogc

xloga = y/2 logc

xloga = y/2 (LOGA + LOGE) = 2

(2x - y)loga = ylogc

loga/logc = y/2x-y (1)

y/2 logac = zlogc

y/2 (loga+logc) = zlogc

yloga = (2z - y)logc

loga/logc = 2z-y/y (2)

(1) = (2)

y/2x-y = 2z-y/y

y² = (2x - y) (2z - y)

4 x z-y (2x + 2z) = 0

2 x 2 − y(x+2) = 0

2/y = 1/z + 1/x

Step-by-step explanation:

anhenseyo sweetums unnie, good morning.