(5−3)2(\sqrt{5} - \sqrt{3})^2(5−3)2 is :
8+2158 + 2\sqrt{15}8+215
8+158 + \sqrt{15}8+15
8−158 - \sqrt{15}8−15
8−2158 - 2\sqrt{15}8−215
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Solving,
⇒(5−3)2⇒(5)2+(3)2−2×5×3⇒5+3−215⇒8−215.\Rightarrow (\sqrt{5} - \sqrt{3})^2 \\[1em] \Rightarrow (\sqrt{5})^2 + (\sqrt{3})^2 - 2 \times \sqrt{5} \times \sqrt{3} \\[1em] \Rightarrow 5 + 3 - 2\sqrt{15} \\[1em] \Rightarrow 8 - 2\sqrt{15}.⇒(5−3)2⇒(5)2+(3)2−2×5×3⇒5+3−215⇒8−215.
Hence, Option 4 is the correct option.
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If x = 1 + 2, then (x+1x)2\sqrt{2}, \text{ then } \Big(x + \dfrac{1}{x}\Big)^22, then (x+x1)2 is :
222\sqrt{2}22
8
4
424\sqrt{2}42
227+31243\dfrac{2\sqrt{27} + 3\sqrt{12}}{4\sqrt{3}}43227+312 is equal to :
232\sqrt{3}23
323\sqrt{2}32
3
3+2\sqrt{3} + \sqrt{2}3+2
34+7\dfrac{3}{4 + \sqrt{7}}4+73 is equal to :
13(4−7)\dfrac{1}{3}(4 - \sqrt{7})31(4−7)
3(4−7)3(4 - \sqrt{7})3(4−7)
13(4+7)\dfrac{1}{3}(4 + \sqrt{7})31(4+7)
3(4+7)3(4 + \sqrt{7})3(4+7)
17−5\dfrac{1}{7 - \sqrt{5}}7−51 is equal to :
4(7+5)4(7 + \sqrt{5})4(7+5)
144(7+5)\dfrac{1}{44}(7 + \sqrt{5})441(7+5)
144(7−5)\dfrac{1}{44}(7 - \sqrt{5})441(7−5)
4(7−5)4(7 - \sqrt{5})4(7−5)
