If x be the real number such that $x^{3} + 4 x = 8$ , then the value of the expression $x^{7} + 64 x^{2}$ is

124

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125

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128

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132

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Solution

The correct option is C $128$
$x$ is the real number such that $x^{3} + 4 x = 8$ .... $(i)$
Now,
$x^{7} + 64 x^{2}$
$= x \times {(x^{3})}^{2} + 64 x^{2}$
$= x \times {(8 - 4 x)}^{2} + 64 x^{2}$ ..... Using $(i)$
$= 64 x + 16 x^{3}$
$= 16 (4 x + x^{3}) = 16 \times 8 = 128$

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