If $x=\frac{(7+5 \sqrt{2})^{\frac{1}{3}}

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $x=\frac{(7+5 \sqrt{2})^{\frac{1}{3}}}{2+2 \sqrt{2}}$, then x belongs to:

Options:

$(2,3)$

$(0,1)$

$(-1,0)$

$(3,4)$

Correct Answer:

$(0,1)$

Explanation:

Cube both the sides, we get

$x^3=\frac{7+5 \sqrt{2}}{8(7+5 \sqrt{2})}=\frac{1}{8}$

$\Rightarrow x=\frac{1}{2}$. Cleary $x$ lies between 0 and 1 .

Hence (2) is the correct answer.