Question

if the mean of p, 1/p is q, then the mean of p3, 1/p^3 is
1) 8q^3- 3q
2) 8q^3- 3q/2
3) q^3 + 3
4) 4q^3- 3q​

Answer 1

Answer:

Mean of $p^3\:and\:\frac{1}{p^3}=4q^3-3q$

option(4) is correct

Step-by-step explanation:

Formula used:

$(a+b)^3=a^3+b^3+3ab(a+b)$

$a^3+b^3=(a+b)^3-3ab(a+b)$

Given:

The mean of $p\:and\:\frac{1}{p}$ is q

Then

$\frac{p+\frac{1}{p}}{2}=q$

$p+\frac{1}{p}=2q$

Now ,

Mean of $p^3\:and\:\frac{1}{p^3}$

$=\frac{p^3+\frac{1}{p^3}}{2}$

$=\frac{p^3+(\frac{1}{p})^3}{2}$

$=\frac{(p+\frac{1}{p})^3-3.p.\frac{1}{p}(p+\frac{1}{p})}{2}$

$=\frac{(2q)^3-3(2q)}{2}$

$=\frac{8q^3-3(2q)}{2}$

$=4q^3-3q$

Answer 2

Answer:

4Q³ - 3Q

Step-by-step explanation:

if the mean of p, 1/p is q, then the mean of p3, 1/p^3 is

Mean of P & 1/P = ( P + 1/P)/2

Q = ( P + 1/P)/2

2Q = (P + 1/P)

Taking cube both side

(2Q)³ = (P + 1/P)³

=> 8Q³ = P³ + 1/P³  + 3P(1/P)( P + 1/P)

=> 8Q³ = P³ + 1/P³ + 3(2Q)

=> P³ + 1/P³ = 8Q³ - 6Q

Dividing by 2 both sides

=> (P³ + 1/P³)/2 = 4Q³ - 3Q

=> Mean of P³ + 1/P³ = 4Q³ - 3Q

option 4 is correct