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Delhi Police Constable Exam Model Paper 4

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Question : 88 of 100

Marks: +1, -0

If

(x-3)^2 + (y+5)^2 + (z-2)^2

= 0, then find the value of

x^3 + y^3 + z^3.

-90
90
-75
75

Solution:

Tips & Tricks

GIVEN:

(x-3)^2 + (y+5)^2 + (z-2)^2 = 0

FORMULA USED:

If x + y + z = 0, then

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

CALCULATION:

Sum of square will be zero ‘0’

only and when they are individually zero ‘0’.

x - 3 = 0

⇒ x = 3And, y + 5 = 0

⇒ y = -5

And, z – 2 = 0

⇒ z = 2

Since

x + y + z = 3 + (-5) + 2 = 0

Hence,

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

= 3 \times 3 \times (-5) \times 2 = -90

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