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CUET PG 2025 Mathematics PYQ — If and , then the value of is:… | Mathem Solvex

A.
-4
(Correct Answer)
B.
4
C.
$3$
D.
$23$

Correct Answer:

-4

Explanation

Maana ki $y = (2+\sqrt{3})^{\frac{1}{3}}$

x = y + \frac{1}{y}

Dono taraf cube karne par:

x^{3} = (y + \frac{1}{y})^{3}

x^{3} = y^{3} + \frac{1}{y^{3}} + 3(y)(\frac{1}{y})(y + \frac{1}{y})

x^{3} = y^{3} + \frac{1}{y^{3}} + 3x

x^{3} - 3x = y^{3} + \frac{1}{y^{3}}

Ab $y^3$ ki value rakhne par:

y^{3} = ((2+\sqrt{3})^{\frac{1}{3}})^{3} = 2+\sqrt{3}

\frac{1}{y^{3}} = \frac{1}{2+\sqrt{3}} = 2-\sqrt{3}

Inhe equation mein rakhne par:

x^{3} - 3x = (2+\sqrt{3}) + (2-\sqrt{3})

x^{3} - 3x = 4

Di gayi equation hai:

x^{3} - 3x + k = 0

4 + k = 0

k = -4

Final Answer:

k = -4

CUET PG 2025 — Mathematics PYQ

Choose the correct answer:

Explanation

Explanation