Question
Download Solution PDFWhich 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Last updated on Jul 9, 2025
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