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If xy = r, xz = r2, yz = r3, x + y + z = 13 and x2 + y2 + z2 = 91, then find z/y.
- A3
- B4
- C7/3
- D13/3
Answer not set
Discussion 1
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CCommunity
x + y + z = 13, on squaring both sides
⇒ x2 + y2 + z2 + 2(xy + yz + zx) = 169
⇒ 2(xy + yz + zx) = 169 – 91 = 78
⇒ (xy + yz + zx) = 39
⇒ (r + r2 + r3) = 39 = 3 + 9 + 27
⇒ r = 3
∴ z/y = xz/xy = r2/r = r = 3
⇒ x2 + y2 + z2 + 2(xy + yz + zx) = 169
⇒ 2(xy + yz + zx) = 169 – 91 = 78
⇒ (xy + yz + zx) = 39
⇒ (r + r2 + r3) = 39 = 3 + 9 + 27
⇒ r = 3
∴ z/y = xz/xy = r2/r = r = 3