SSC CPO 2020 PYQ — Question 135

The correct answer is Option 4 i.e. -6.

We know that,

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - (xy + yz + zx)).........(1)

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)...........(2)

Now, according to the question

From Equation (2)

⇒ 13² = 133 + 2(xy + yz + zx)

⇒ 169 - 133 = 2(xy + yz + zx)

⇒ (xy + yz + zx) = 36/2

⇒ (xy + yz + zx) = 18

Put all the values in Equation (1);

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - (xy + yz + zx))

⇒ 847 - 3xyz = 13(133 - 18)

⇒ 847 - 115 × 13 = 3(xyz)

⇒ - 648 = 3(xyz)

⇒ - 216 = xyz

⇒ - (216)^1/3 = (xyz)^1/3

⇒ - (216)^1/3 = ³√xyz

So, the value of ³√xyz = - 6