Discussion

Explanation:

Square root of 5 + √21 will be of the form √x + √y.

∴ (√x + √y)² = 5 + √21

⇒ x + y + 2√xy = 5 + √21

Now, rational part of RHS = rational part on LHS
⇒ x + y = 5   …(1)

Also, irrational part of RHS = irrational part on LHS
⇒ 2√xy = √21
⇒ xy = 21/4   …(2)

⇒ x(5 - x) = 21/4 [From (1)]
⇒ 4x² - 20x + 21 = 0
⇒ x = 3/2 or 7/2

∴ x = 7/2 and y = 3/2 or x = 3/2 and y = 7/2.

In both cases square root of 5 + √21 = $\sqrt{\frac{7}{2}}+\sqrt{\frac{3}{2}}$

Hence, option (c).

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