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:

Question 129

Solution

Given : $$x(x+y+z)=20$$

=> $$x^2+xy+xz=20$$ -----------------(i)

Similarly, => $$y^2+xy+yz=30$$ -----------------(ii)

and $$z^2+xz+yz=50$$ -----------------(iii)

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

=> $$(x^2+y^2+z^2)+2(xy+yz+xz)=20+30+50$$

=> $$(x+y+z)^2=100$$

=> $$(x+y+z)=\sqrt{100}=10$$

$$\therefore$$ $$2(x+y+z)=2\times10=20$$

=> Ans - (D)

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