Question : Which of the following statements is correct?
I. If $x = 12, y = -2$ and $z = -10$, then $x^3+y^3+z^3=720$
II. If $x + y = 48$ and $4xy =128$, then the value of $4x^2+4y^2$ is 8960
Option 1: Neither I nor II
Option 2: Only I
Option 3: Both I and II
Option 4: Only II
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Correct Answer: Both I and II
Solution :
I. $x = 12, y = -2, z = -10$
$x^3+y^3+z^3$
$= 12^3 + (-2)^3 + (-10)^3$
$=1728-8-1000$
$=720$
So, $x^3+y^3+z^3=720$
II. $x + y = 48$
⇒ $4xy =128$
⇒ $xy = 32$
⇒ $4x^2+4y^2=4(x^2+y^2)$
$=4[(x+y)^2-2xy]$
$=4[48^2-2×32]$
$=9216-256$
$=8960$
S0, $4x^2+4y^2=8960$
Hence, the correct answer is Both I and II.
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