If x + y + z = 13, x2 + y2 + z2 = 91 and xz = y2, then the difference between z and x is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 8.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)la
⇒ 132 = 91 + 2(xy + yz + xz)
⇒ 169 - 91 = 2(xy + yz + y2)
⇒ 39 = y(x + y + z)
⇒ y = 3
So, y2 = 9 --(i)
From (i)
xz = 9
So, we get x = 9, z = 1, y = 3
Difference x and z = 9 - 1 = 8