Question : If $x=(\sqrt[3]{7})^{3}+3$, then the value of $x^3–9x^2+27x–34$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –1
Answer (1)
25th Jan, 2024
Correct Answer: 0
Solution :
Given: $(x–3)^{3}=(\sqrt[3]{7})^{3}$
$x^{3}–27–3(3x)(x–3) = 7$
$x^{3}–27–9x^{2}+27x = 7$
Subtracting 7 on both sides, we get,
$x^{3}–27–9x^{2}+27x–7= 7–7$
$x^{3}–9x^{2}+27x–34 = 0$
Hence, the correct answer is 0.
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