Question

If x,y,z are in continued proportion then x² = ?

Answer 1

If x, y, z are in continued proportion ( x : y :: y : z) then y² = xz

y² = xz

=> x = y² / z

=> x² = ( y²/z)²

=> x² = $\frac{ {y}^{4} }{ {y}^{2} }$

hope helped! ^^

Answer 2

Hey there !!
Thank u for ur Question

First of all i just clear it what Continued Proportion is by taking an example -

Continued proportion : Three numbers ‘a’, ‘b’ and ‘c’ are said to be continued proportion if a, b and c are in proportion. 
Thus, if a, b and c are in continued-proportion, then 
a,b,b,c are in proportion, that means 
a : b : : b : c 
⇒ Product of extremes = Product of means 
⇒ a x c = b x b 
⇒ ac = b^2
Continued-proportion is also known as mean proportional .
If ‘b’ is a mean proportional between a and c then b2 = ac. ....1)

Now coming to the given Question where -
we need to find out of
${x}^{2}$
so , By equation 1)

${y}^{2} = xz \\ = > x = \frac{ {y}^{2} }{z} \\ = > {x}^{2} = \frac{ { {y}^{2} }^{2} }{z} (squaring \: both \: side) \\ \\ hence \: \: \: {x}^{2} \: = \frac{ {y}^{4} }{ {z}^{2} }$
Hope this helps u!!!