Question

If 4a^2b, 8ab^2, p are in continued proportion then find the value of p

Answer 1

SOLUTION :

GIVEN

$\sf{ 4 {a}^{2}b ,8a {b}^{2} ,p\: \: are \: in \: continued \: proportion}$

TO DETERMINE

The value of p

CONCEPT TO BE IMPLEMENTED

If three numbers a, b, c are in continued proportion then

a : b = b : c

EVALUATION

It is given that

$\sf{ 4 {a}^{2}b ,8a {b}^{2} ,p\: \: are \: in \: continued \: proportion}$

Hence

$\sf{ 4 {a}^{2}b : 8a {b}^{2} =8a {b}^{2} : p}$

$\implies \displaystyle \sf{ \frac{4 {a}^{2}b }{8a {b}^{2}} \: } = \sf{ \frac{8a {b}^{2}}{p} }$

$\implies \displaystyle \sf{ p \times {4 {a}^{2}b } = {8a {b}^{2}} \: } \times \sf{{8a {b}^{2}} }$

$\implies \displaystyle \sf{ p \times {4 {a}^{2}b } = 64 {a}^{2} {b}^{4} }$

$\implies \displaystyle \sf{ p = 16 {b}^{3} }$

RESULT

Hence the required answer is

$\boxed{ \displaystyle \sf{ \: \: p = 16 {b}^{3} \: }}$

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LEARN MORE FROM BRAINLY

If x=√3a+2b + √3a-2b / √3a+2b - √3a-2b

Then prove that bx²-3ax+b=0

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