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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Question : Which of the following statements is correct? I. If $x=12, y=-2$ and $z=-10$, then $x^3+y^3+z^3=360$. II. If $x+y=48$ and $4 x y=128$, then $4 x^2+4 y^2=4480$.
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