SSC CGL Model Paper 14

Question : 63 of 100

Marks: +1, -0

(x + y + z) = 12

xy + yz + zx = 44

and xyz = 48, then what is the value of

x^ 3 + y^ 3 + z^3

Solution:

x + y + z = 12,

xy + yz + zx= 4 4

xyz =48

(x + y + z )^2

= x^ 2 + y ^2 + z ^2

+ 2 (xy + y z + zx)

⇒ (12)^2 = x ^2 + y^ 2

+ z ^2 + 2 × 44

⇒ x ^2 + y^ 2 + z^ 2

= 144 - 88 = 56

x^ 3 + y ^3 + z ^3 -3 x y z

= (x + y + z)

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

⇒ x^ 3 + y ^3 + z^ 3 - 3 × 48

= 12 × (5 6 -4 4 )

∴ x^3 + y ^3 + z ^3

= 12 × 12 + 144

= 144 + 144=288

Go to Question:

Prev Question

Next Question