Question

If (8/15)^3 - (1/3)^3 - (1/5)^3 = x/75, find x.

Answer 1

Hi ,

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We know that ,

If a + b + c = 0 then

a³ + b³ + c³ = 3abc

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Here ,

Let a = 8/15 ,

b = - 1/3 ,

c = - 1/5 ,

a + b + c

= 8/15 - 1/3 + 1/5

= ( 8 - 5 - 3 ) / 15

= 0

Therefore ,

a + b + c = 0 ----( 1 )

Now ,

( 8/15 )³ + ( -1/3 )³ + ( - 1/5 )³ = x/75

3 ( 8/15 ) ( - 1/3 ) ( - 1/5 ) = x /75

After cancellation ,

8 = x

Therefore ,

x = 8

I hope this helps you.

: )