Question

Find the value of the unknown numbers if they are in continued proportion 1 = 8,x,32,y

Answer 1

SOLUTION

TO DETERMINE

The value of x and y when 8 , x , 32 , y are in continued proportion

EVALUATION

Here it is given that 8 , x , 32 , y are in continued proportion

So by the given condition

$\sf{8 : x = x : 32 = 32 : y}$

Now

$\sf{8 : x = x : 32 } \: \: \: \: \: gives$

$\displaystyle \sf{ \frac{8}{x} = \frac{x}{32} }$

$\implies \: \displaystyle \sf{ {x}^{2} = 8 \times 32 }$

$\implies \: \displaystyle \sf{ {x}^{2} = 16 \times 16}$

$\implies \: \displaystyle \sf{ x = \pm \: 16 }$

Now

$\sf{x : 32 = 32 : y}$

$\displaystyle \sf{ \frac{x}{32} = \frac{32}{y} }$

$\implies \displaystyle \sf{ xy = 32 \times 32 }$

Now x = 16 gives y = 64

Again x = - 16 gives y = - 64

FINAL ANSWER

Hence the required values is

• x = 16 , y = 64

• x = - 16 , y = - 64

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Ifa : b=c:d=e: f= 2:1,

then (a + 2c + 3e) : (5b + 10d + 15f) is equal to:

https://brainly.in/question/23293448

2. X,Y,Z,W are 4:3:2:1 .Z acquire 1/5 from X. Y acquire 1/5 from X and W equally . Find new ratio and sacrifice ratio

https://brainly.in/question/21221028

Answer 2

SOLUTION

TO DETERMINE

The value of x and y when 8 , x , 32 , y are in continued proportion

EVALUATION

Here it is given that 8 , x , 32 , y are in continued proportion

So by the given condition

8:x=x:32=32:y

Now

gives8:x=x:32gives

8/x

= x/32

⟹x²

=8×x²

⟹x ²

=16×16

⟹x=±16

Now

x:32=32:y

32/x=32/y

⟹xy=32×32

Now x = 16 gives y = 64

Again x = - 16 gives y = - 64

FINAL ANSWER

Hence the required values is

x = 16 , y = 64

x = - 16 , y = - 64

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Ifa : b=c:d=e: f= 2:1,

then (a + 2c + 3e) : (5b + 10d + 15f) is equal to:

https://brainly.in/question/23293448

2. X,Y,Z,W are 4:3:2:1 .Z acquire 1/5 from X. Y acquire 1/5 from X and W equally . Find new ratio and sacrifice ratio

https://brainly.in/question/21221028