Question

Maths question
If (x-1)^(3)+(y-2)^(3)+(z-3)^(3)=3(x-1)(y-2)(z-3) and x-1 is not equal to y-2 is not equal to z-3 then x+y+z is equal to?
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Answer 1

Step-by-step explanation:

Given :-

(x-1)³+(y-2)³+(z-3)³ =3(x-1)(y-2)(z-3)

To find :-

Find the value of x+y+z ?

Solution :-

Given equation is

(x-1)³+(y-2)³+(z-3)³=3(x-1)(y-2)(z-3)

Where , x-1 ≠ y-2 ≠z-3

It is in the form of a³+b³+c³ = 3abc

Where, a = x-1

b = y-2

c = z-3

We know that

If a+b+c = 0 then a³+b³+c³ = 3abc

So, (x-1)³+(y-2)³+(z-3)³=3(x-1)(y-2)(z-3)

=> (x-1)+(y-2)+(z-3) = 0

=> x+y+z-1-2-3 = 0

=> x+y+z-6 = 0

=> x+y+z = 6

Therefore, x+y+z = 6

Answer:-

The value of x+y+z for the given problem is 6

Used formulae:-

→If a+b+c = 0 then a³+b³+c³ = 3abc