If x=8−60, then 12(x+2x) is

x=8−60 x=8−4×15 =8−25×3 x=(5−3)⋯⋯(1) Also,1x=15−3×5+35+3 1x=5+32 2x=(5+3)⋯⋯(2) 12(x+2x)=12(25)=5

If x=8−60, then 12(x+2x) is

x=8−60 x=8−4×15 =8−25×3 x=(5−3)⋯⋯(1) Also,1x=15−3×5+35+3 1x=5+32 2x=(5+3)⋯⋯(2) 12(x+2x)=12(25)=5

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If $x = 8 - \sqrt{60}$ , then $\frac{1}{2} (\sqrt{x} + \frac{2}{\sqrt{x}})$ is

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$\sqrt{5}$

$\sqrt{3}$

$2 \sqrt{3}$

$2 \sqrt{5}$

answer is A.

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Detailed Solution

$x = 8 - \sqrt{60} \sqrt{x} = \sqrt{8 - \sqrt{4 \times 15}} = \sqrt{8 - 2 \sqrt{5 \times 3}} \sqrt{x} = (\sqrt{5} - \sqrt{3}) \dots \dots (1) Also, \frac{1}{\sqrt{x}} = \frac{1}{\sqrt{5} - \sqrt{3}} \times \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}} \frac{1}{\sqrt{x}} = \frac{\sqrt{5} + \sqrt{3}}{2} \frac{2}{\sqrt{x}} = (\sqrt{5} + \sqrt{3}) \dots \dots (2) \frac{1}{2} (\sqrt{x} + \frac{2}{\sqrt{x}}) = \frac{1}{2} (2 \sqrt{5}) = \sqrt{5}$