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If x (x + y + z) = 20, y (x + y + z) = 30, and z (x + y + z) = 50, then the value of 2 (x + y + z) is :
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- 20
- –10
- 15
- 18
Correct Option: B
x (x + y + z) = 20
⇒ x2 + xy + xz = 20 --- (i)
Again, y (x + y + z) = 30
⇒ xy + y2 + yz = 30 --- (ii)
and, z (x + y + z) = 50
⇒ xz + yz + z2 = 50 --- (iii)
On adding all three equations,
x2 + y2 + z2 + 2xy + 2yz + 2zx = 20 + 30 + 50
⇒ (x + y + z)2 = 100
⇒ x + y + z = 10
⇒ 2 (x + y + z) = 20
