Which of the following statement is correct?

I. If x = 12, y = -2 and z = -10, then x3 + y3 + z3 = 360.

II. If x + y = 48 and 4xy = 128, then 4x2 + 4y2 = 4480.

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SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 1)
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  1. Neither I nor II
  2. Only I
  3. Both I and II
  4. Only II

Answer (Detailed Solution Below)

Option 1 : Neither I nor II
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Detailed Solution

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Given:

I. If x = 12, y = -2 and z = -10, then x3 + y3 + z3 = 360.

II. If x + y = 48 and 4xy = 128, then 4x2 + 4y2 = 4480.

Concept used:

a2 + b2 + 2ab = (a + b)2

Calculation:

I.  x3 + y3 + z3 

⇒ (12)3 + (-2)3 + (-10)3 

⇒ 1728 - 8 - 1000

⇒ 720

II. Here, 4xy = 128

⇒ 2xy = 64      ....(1)

x + y = 48

⇒ (x + y)2 = 482

⇒ x2 + y2 + 2xy = 2304

⇒ x2 + y2 = 2304 - 64 (From 1)

⇒ x2 + y2 = 2240

⇒ 4x2 + 4y2 = 4 × 2240

⇒ 4x2 + 4y2 = 8960

Hence, neither I nor II follows.

∴ Neither I nor II is correct.

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