SarkariPYQ

SSC CGL 2021 PYQ — Question 52

SSC CGL - 20 Aug 2021 - Shift 3 • Quantitative Aptitude • Q52

Back to paper

If x + y + z = 3, xy + yz + zx = -12 and xyz = -16, then the value of x3+y3+z3+13\sqrt{x^3+y^3+z^3+13} is:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 10.

It is given that x + y + z = 3,

On squaring both sides we get,

⇒ x2 + y2 + z2 + 2(xy + yz + zx) = 9

⇒ x2 + y2 + z2  = 9 + 24 = 33.

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

⇒ x3 + y3 + z3 - 3xyz = 3 × (33 + 12)

⇒ x3 + y3 + z3 - 3 × -16 = 3 × 45

⇒ x3 + y3 + z3 = 135 - 48 = 87

⇒ x3+y3+z3+13\sqrt{x^3+y^3+z^3+13} 

= 87+13=10\sqrt{87 + 13} = 10.