Question

The numbers a, b, c are in continued proportion in order. If a = 4 and c = a x a, find b ​

Answer 1

Answer:

6

Step-by-step explanation:

a = 4

c = 4*4 =8

b= (no. between a and c)

: 6

1. think so it is right

Answer 2

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FORMULA TO BE IMPLEMENTED

The numbers a, b, c are in continued proportion in order if

$\sf{ a : b = b : c\: }$

$\displaystyle \: \implies \: \frac{a}{b} = \frac{b}{c}$

$\displaystyle \: \implies \: {b}^{2} = ac$

GIVEN

1. The numbers a, b, c are in continued proportion in order

$2. \: \: \sf{ \: a = 4}$

$3. \: \sf{ \: c = a \times a }$

TO DETERMINE

The value of b

EVALUATION

Since The numbers a, b, c are in continued proportion in order

So by the above mentioned formula

$\sf{ \displaystyle \: \implies \: {b}^{2} = ac}$

$\sf{ \displaystyle \: \implies \: {b}^{2} = a \times a \times a}$

$\sf{ \displaystyle \: \implies \: {b}^{2} = {a}^{3} }$

$\sf{ \displaystyle \: \implies \: {b}^{2} = {(4)}^{3} }$

$\sf{ \displaystyle \: \implies \: {b}^{2} = 64}$

$\sf{ \displaystyle \: \implies \: b = \pm \: 8 \: }$

RESULT

The required answer is

$\boxed{ \: \sf{ \: b = \pm \: 8 \: } \: }$