Option 4 : 8

**Given **

If x + y + z = 13,

x2 + y2 + z2 = 91

**Formula Used **

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)

**Calculation **

Using above formula

⇒ 13^{2} = 91 + 2(xy + yz + xz)

⇒ 169 - 91 = 2(xy + yz + y^{2}) [We know, xz = y^{2}]

⇒ 39 = y(x + y + z)

⇒ y = 3

So, y^{2} = 9 ...(i)

From (i)

xz = 9

So, we get x = 9, z = 1, y = 3

Difference x and z = 9 - 1 = 8

**∴ The required answer is 8 **

__Alternate Method__

x + y + z = 13

x2 + y2 + z2 = 91

From both equation

We can assume x = 9, y = 3 and z = 1

xz = y^{2}

satisfy the equation

So, Difference in x and z = 9 - 1 = 8