Question

(a - 1/a) = 3/4 so find (a³ - 1/a³)​

Answer 1

Solution

Given :-

• a - 1/a = 3/4_______(1)

Find :-

• Value of ( a³ - 1/a³ )

Explanation

Using Formula

★ ( x³ - y³) = (x - y)(x² + xy + y²)

★ ( x - y)² = x² - 2xy + y²

So, squaring both side of equ(1)

==> (a - 1/a )² = (3/4)²

==> a² + 1/a² - 2 = 9/16

==> a² + 1/a² = 9/16 + 2

==> a² + 1/a² = (9 + 32)/16

==> a² + 1/a² = 41/16_________(2)

Now, Calculate ( a³ - 1/a³)

==> ( a³ - 1/a³) = ( a - 1/a)(a² + 1/a² + 1)

keep Value,

==> ( a³ - 1/a³) = (3/4)( 41/16 + 1)

==> ( a³ - 1/a³) = (3/4) [ 41 + 16)/16]

==> ( a³ - 1/a³) = 3/4 ( 57/16)

==> ( a³ - 1/a³) = 171/64

Hence

• Value of ( a³ - 1/a³) will be = 171/64

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Answer 2

Step-by-step explanation:

Answer

Given:-

• a-1/a=3/4________(1)

Find:-

• value of (a³ - 1/a³)

Explanation:-

using formula

➥(x³-y³)=(x-y) (x²+xy+y²)

➥(x-y)²=x²-2×y+y²

So, squaring in both side of eqn (1)

➝(a-1/a)²=(3/4)²

➝a²+1/a²-2=9/16

➝a²+1/a²=9/16-12

➝a²+1/a²=9/16-2

➝a²+1/a²=(9+32)/16

➝a²+1/a²=41/16________(2)

Now ,Calculate (a³-1/a³)

➝(a³-1/a³)= (a-1/a) (a²+1/a²+1)

keep Value,

➝(a³-1/a³)= (3/4) (41/16+1)

➝(a³-a³)= [ (3/4) (41+16)/16 ]

➝(a³-1)a³)= 3/4 [ 57 /16 ]

➝(a³-171/64

Hence,

$\bf \pink{Value of (a³ - 1/a³)will be 171/64}$

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