if 4ab2, 8a2b, p are in continued proportion then find the value of p
Answers
Answer:
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}4a
2
b,8ab
2
,pareincontinuedproportion
Hence
\sf{ 4 {a}^{2}b : 8a {b}^{2} =8a {b}^{2} : p}4a
2
b:8ab
2
=8ab
2
:p
\implies \displaystyle \sf{ \frac{4 {a}^{2}b }{8a {b}^{2}} \: } = \sf{ \frac{8a {b}^{2}}{p} }⟹
8ab
2
4a
2
b
=
p
8ab
2
\implies \displaystyle \sf{ p \times {4 {a}^{2}b } = {8a {b}^{2}} \: } \times \sf{{8a {b}^{2}} }⟹p×4a
2
b=8ab
2
×8ab
2
\implies \displaystyle \sf{ p \times {4 {a}^{2}b } = 64 {a}^{2} {b}^{4} }⟹p×4a
2
b=64a
2
b
4
\implies \displaystyle \sf{ p = 16 {b}^{3} }⟹p=16b
3
RESULT
Hence the required answer is
\boxed{ \displaystyle \sf{ \: \: p = 16 {b}^{3} \: }}
p=16b
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
Step-by-step explanation:
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