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RRB Group D 1 Dec 2025 Shift 2 Solved Paper

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Question : 39 of 100

Marks: +1, -0

If

(a-1)^{3}+(a-4)^{3}+(a-7)^{3}=3(a-1)(a-4)(a-7)

, find the value of

a

.

$-4$
1
4
$-1$

Solution:

Concept:

If

x^3 + y^3 + z^3 = 3xyz

, then

x + y + z = 0

.

Explanation:

Let

x = a-1

,

y = a-4

, and

z = a-7

.

The given equation becomes

x^3 + y^3 + z^3 = 3xyz

.

Using the identity, we get

x + y + z = 0

.

Therefore,

(a-1) + (a-4) + (a-7) = 0

.

Simplify:

3a - 12 = 0

.

So

3a = 12

, which gives

a = 4

.

Answer:

a = 4

(Option C).

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