22. If x = 7-413 and the value of (...
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22. If x = 7-413 and the value of (1) 0 (3) 4 RRB NTPC (Phase I) 2016 (2) 1 (4) – 4

11th - 12th Class
Maths
Solution
105
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( x=7-4 sqrt{3} ) ( Rightarrow sqrt{x}+frac{1}{sqrt{x}} ) ( Rightarrow sqrt{7-4 sqrt{3}}+frac{1}{sqrt{7-4 sqrt{3}}} ) ( Rightarrow sqrt{(2)^{2}+(sqrt{3})^{2}-2(2)(sqrt{3})}+frac{1}{sqrt{(2)^{2}+(sqrt{3})^{2}-2(sqrt{3})(2)}} ) ( Rightarrow sqrt{(2-sqrt{3})^{2}}+frac{1}{sqrt{(2-sqrt{3})^{2}}} ) ( Rightarrow(2-sqrt{3})+frac{1}{(2-sqrt{3})} ) Taking LaM ( Rightarrow frac{(2-sqrt{3})^{2}+1}{(2-sqrt{3})} ) ( Rightarrow frac{4+3-4 sqrt{3}+1}{2-sqrt{3}} ) ( Rightarrow quad frac{8-4 sqrt{3}}{2-sqrt{3}} )
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