Question

1
Q10. Orphanages owners often need extra support. By helping such
organisations to take on more children and provide better care, we can
have good impact on the society. For this Ram donated Rs. (x3 + 3) to an
orphanage children. His friend Shyam wanted to know the amount
donated by him. Ram did not disclose the amount but he gave a clue that
x + 1/X = Rs.8

if x-1/X=4, find the value of x^3-1/x^3​

Answer 1

Answer:

₹ 488

Step-by-step explanation:

($x$³ + $\frac{1}{x}$³) =========> Amt. donated by Ram

($x$ + $\frac{1}{x}$) =============> 8

So first, we cube on both sides -

($x$ + $\frac{1}{x}$)³= (8)³

Now, after expanding ($x$ + $\frac{1}{x}$)

according to the formula - (a + b)³ = a³ + b³ + 3ab (a + b), we get -

$x$³ + $\frac{1}{x}$³ + (3 × $x$ × $\frac{1}{x}$)($x$ + $\frac{1}{x}$)

Now, because we already know, that ($x$ + $\frac{1}{x}$ = 8, we can replace it with 8)

$x$³ + $\frac{1}{x}$³ + (3 × $x$ × $\frac{1}{x}$) (8)

Now, in '3 × $x$ × $\frac{1}{x}$', $x$ and $x$ will get cancelled

After which, we'll get this equation -

$x$³ + $\frac{1}{x}$³+ (3 × 8) = 512

$x$³ + $\frac{1}{x}$³ + 24 = 512

Now, after transposing, we get

$x$³ + $\frac{1}{x}$³ = 512 - 24

Therefore, we get the answer as

$x$³ + $\frac{1}{x}$³ = 488

And yes, don't forget to add the sign - ₹488

Hope you found it useful...

Thank you