Question

If x-1by x is equal to 7 then find value of x^3 -1/x^3

Answer 1

Step-by-step explanation:

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Answer 2

Question

If x-1/x = 7 , then find value of x³ -1/x³ .

Solution

Given:-

• x - 1/x = 7 -----------(1)

Find:-

• Value of x³ - 1/x³ .

Explanation

Using Formula

★ (a -b)² = (a²-2ab+b²)

★ (a³-b³) = (a-b)(a²+b²+ab)

Squaring both side of equation (1)

==>(x - 1/x)² = 7²

==> (x² + 1/x² + x * 1/x ) = 49

==> x² + 1/x² = 49 - 1

==> x² + 1/x²= 48 -------------(2)

Now, Using Second Formula,

==> (x³ - 1/x³) = (x - 1/x) (x² + 1/x² + x * 1/x)

==>(x³ - 1/x³) = (x - 1/x) (x² + 1/x² + 1)

Keep values by equ(1) &(2)

==> (x³ - 1/x³) = (7) * (48 + 1)

==>(x³ - 1/x³) = 7 * 49

==>(x³ - 1/x³) = 343. [Ans]

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