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STD 11 - 7. binomial theoram — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 7. binomial theoram4 Marks
MCQ
Let $x=(\sqrt{50}+7)^{1 / 3}-(\sqrt{50}-7)^{1 / 3}$. Then,
  • ✓
    $x=2$
  • B
    $x=3$
  • C
    $x$ is a rational number, but not an integer
  • D
    $x$ is an irrational number
✓

Answer

Correct option: A.
$x=2$
a
(a)

Given,

$x=(\sqrt{50}+7)^{1 / 3}-(\sqrt{50}-7)^{1 / 3}$

On cubing both sides, we get

$x^3=(\sqrt{50}+7)-(\sqrt{50}-7)-3$

$(\sqrt{50}+7)^{1 / 3}(\sqrt{50}-7)^{1 / 3}$

${\left[(\sqrt{50}+7)^{1 / 3}-(\sqrt{50}-7)^{1 / 3}\right] }$

$\Rightarrow \quad x^3=14-3(50-49)^{1 / 3}(x)$

$\Rightarrow \quad x^3=14-3 x$

$\Rightarrow \quad x^3+3 x-14=0$

$\Rightarrow(x-2)\left(x^2+2 x+7\right)=0$

$\Rightarrow \quad x=2$

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