Question

If a-1/a=4, find the value of a³-1/a³

Answer 1

If a-1/a = 4 .

then, [a -1/a]^3 = (4)^3

a^3 - 1/a^3 - 3a×1/a(a - 1/a) = 64

a^3 -1/a^3 -3(4) = 64. (putting the value of a -1/a).

a^3 -1/a^3 -12 =125

a^3 - 1/a^3 = 125 + 12 = 137.

Answer 2

Answer:

If a-1/a=4, find the value of a³-1/a³ = 76

Step-by-step explanation:

Given :

Since we are given the expression

such that   $a-\frac{1}{a}=4$                                   ..................Equation(1)

To Find :

The value of

$a^3-\frac{1}{a^3}$

Solution :

Since we are given that expression

$a-\frac{1}{a}=4$

taking power 3 both sides of the given expression

$(a-\frac{1}{a})^3=(4)^3$

Since we know that  $(x-y)^3=x^3-y^3-3xy(x-y)$

according the inequality

$a^3-(\frac{1}{a})^3-3(a)(\frac{1}{a})(a-\frac{1}{a})=64$

$a^3-\frac{1}{a^3}-3(4)=64$                                   (substituting value of Equation(1))

$a^3-\frac{1}{a^3}=64+12$

$a^3-\frac{1}{a^3}=76$

Hence we have calculated the vale of

$a^3-\frac{1}{a^3}=76$

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