SSC CHSL 16 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

© examsiri.com

Question : 63 of 100

Marks: +1, -0

If

x+y+z=4, x y+y z+z x=1

and

x^{3}+y^{3}+z^{3}=34

, then what is the value of

2 x y z

?

$-6$
$-12$
8
18

Solution:

Given,

x+y+z=4

,

x y+y z+z x=1

and

x^{3}+y^{3}+z^{3}=34

We know,

(x+y+z)^{2}=x^{2}+y^{2}+z^{2}

+2(x y+y z+z x)

∴ (4)^{2}=x^{2}+y^{2}+z^{2}+2 ×(1)

⇒ x^{2}+y^{2}+z^{2}=16-2=14

Now, we know that,

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)]

⇒ 34-3 x y z=4 ×[14-1]

=4 × 13=52

x y z=\;{-18}/{3}=-6

∴ \;\; 2 x y z=-6 × 2=-12

© examsiri.com

Go to Question:

Prev Question

Next Question