1.

If x + y + z = 5, x2 + y2 + z2 = 21 and y2 = zx, then the value of y is:1.  1/52. 2/53. 1/24. 1/4

Answer» Correct Answer - Option 2 : 2/5

Given:

x + y + z = 5

x2 + y2 + z2 = 21

y2 = zx

Formula used:

(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + xz)

Calculations:

(x + y + z)2 = 52

⇒ x2 + y2 + z2 + 2(xy + yz + xz) = 25

⇒ 21 + 2(xy + yz + xz) = 25

⇒ 2(xy + yz + xz) = 25 - 21

⇒ xy + yz + xz = 4/2

⇒ xy + yz + xz = 2

⇒ xy + yz+ y2 = 2

⇒ y(x + y + z) = 2

⇒ y(5) = 2

⇒ y = 2/5

∴ The required value of y = 2/5


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