SSC CHSL 6 Dec 2015 Shift 1 Paper

Question : 129 of 200

Marks: +1, -0

If x (x+y+z) = 20, y (x+y+z) = 30, & z(x+y+z)=50, then the value of 2(x+y+z) is:

Solution:

Given :

x(x + y + z) = 20

⇒

x ^2 + xy + xz = 20

------(i)
Similarly, ⇒

y^2 + xy + yz = 30

--------(ii)
and

z^2 + xy + yz = 50

--------(iii)
Adding equations (i), (ii) and (iii), we get :
⇒

(x ^2 + y ^2 + z^ 2) + 2(xy + yz + xz)

= 20 + 30 + 50

⇒

(x + y + z) ^2 = 100

⇒

(x + y + z) =√ 100 = 10

∴

2(x + y + z) = 2 × 10 = 20

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