If $a^{1 / x} = b^{1 / y} = c^{1 / z}$ and a , b , c be in G . P . then x , y , z, in H . P .

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B False
Let
$a^{1 / x} = b^{1 / y} = c^{1 / z} = k$

So,
$a = k^{x}, b = k^{y}, c = k^{z}$

Since,
$a, b, c$ are in $G . P$

So,
$b^{2} = a c$

Now,
$k^{2 y} = k^{x} . k^{z}$
$k^{2 y} = k^{x + z}$

Therefore,
$2 y = x + z$

Hence, $x, y, z$ are in $A . P$

Suggest Corrections

Similar questions

a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}}

a^{1 / x} = b^{1 / y} = c^{1 / z}

x, y, z

a, b, c

a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}},

x, y, z

a, b, c

a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{x}}

x, y, z

If $a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}}$ and $a, b, c$ are in G.P., then which of the following are true?

Join BYJU'S Learning Program