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)
13 Likes
Rationalizing,
⇒17−5×7+57+5⇒7+5(7)2−(5)2⇒7+549−5⇒144(7+5).\Rightarrow \dfrac{1}{7 - \sqrt{5}} \times \dfrac{7 + \sqrt{5}}{7 + \sqrt{5}} \\[1em] \Rightarrow \dfrac{7 + \sqrt{5}}{(7)^2 - (\sqrt{5})^2} \\[1em] \Rightarrow \dfrac{7 + \sqrt{5}}{49 - 5} \\[1em] \Rightarrow \dfrac{1}{44}(7 + \sqrt{5}).⇒7−51×7+57+5⇒(7)2−(5)27+5⇒49−57+5⇒441(7+5).
Hence, Option 2 is the correct option.
Answered By
8 Likes
(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
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)
If x = 2−1, then (x−1x)2\sqrt{2} - 1, \text{ then } \Big(x - \dfrac{1}{x}\Big)^22−1, then (x−x1)2 is :
222\sqrt{2}22
2
4
2−22 - \sqrt{2}2−2
5−75+7−5+75−7\dfrac{5 - \sqrt{7}}{5 + \sqrt{7}} - \dfrac{5 + \sqrt{7}}{5 - \sqrt{7}}5+75−7−5−75+7 is equal to :
10710\sqrt{7}107
197\dfrac{1}{9}\sqrt{7}917
1079\dfrac{10\sqrt{7}}{9}9107
−1079-\dfrac{10\sqrt{7}}{9}−9107
