19+6+19−$$6\frac{1}$${9 + $$\sqrt{6}$$} + $$\frac{1}$${9 - $$\sqrt{6}$$}9+61+9−61 = ?

Given:Expression: 19+6+19−$$6\\frac{1}$${9 + $$\\sqrt{6}$$} + $$\\frac{1}$${9 - $$\\sqrt{6}$$}9+61+9−61Formula Used:1a+b+1a−b=2aa2−b$$2\\frac{1}{a + b}$$ + $$\\frac{1}{a - b}$$ = $$\\frac{2a}{a^2 - b^2}$$a+b1+a−b1=a2−b22aSolution:19+6+19−6 =1(9+6)(9−6) =9−6+9+6(9)2−(6)2 =9+981−6 =1875=$$625\\frac{1}$${9 + $$\\sqrt{6}$$} + $$\\frac{1}$${9 - $$\\sqrt{6}$$} \\\\ \\ \\\\ = $$\\frac{1}$${(9 + $$\\sqrt{6}$$)(9 - $$\\sqrt{6}$$)} \\\\ \\ \\\\ = \\frac{9 - $$\\sqrt{6}$$ + 9 + $$\\sqrt{6}$$}{(9)^2 - ($$\\sqrt{6}$$)^2} \\\\ \\ \\\\ = $$\\frac{9 + 9}{81 -6}$$ \\\\ \\ \\\\ = $$\\frac{18}{75}$$ = $$\\frac{6}{25}9$$+61+9−61 =(9+6)(9−6)1 =(9)2−(6)29−6+9+6 =81−69+9 =7518=256Final AnswerSo the correct answer is (c)

19+6+19−6\frac{1}{9 + \sqrt{6}} + \frac{1}{9

Correct option is C

Given:
Expression: $\frac{1}{9 + \sqrt{6}} + \frac{1}{9 - \sqrt{6}}$
Formula Used:
$\frac{1}{a + b} + \frac{1}{a - b} = \frac{2a}{a^2 - b^2}$
Solution:
$\frac{1}{9 + \sqrt{6}} + \frac{1}{9 - \sqrt{6}} \\ \ \\ = \frac{1}{(9 + \sqrt{6})(9 - \sqrt{6})} \\ \ \\ = \frac{9 - \sqrt{6} + 9 + \sqrt{6}}{(9)^2 - (\sqrt{6})^2} \\ \ \\ = \frac{9 + 9}{81 -6} \\ \ \\ = \frac{18}{75} = \frac{6}{25}$
Final Answer
So the correct answer is (c)

$\frac{1}{9 + \sqrt{6}} + \frac{1}{9 - \sqrt{6}}$ = ?

7/24

9/25

6/25

9/19

Correct option is C

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19+6+19−6\frac{1}{9 + \sqrt{6}} + \frac{1}{9 - \sqrt{6}}9+6​1​+9−6​1​ = ?

7/24

9/25

6/25

9/19

Correct option is C

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SSC GD PYP (Held on 4 Feb 2025 S1)

Hindi Section Test 1

SSC GD Constable Full Mock Test 1

Similar Questions

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$\frac{1}{9 + \sqrt{6}} + \frac{1}{9 - \sqrt{6}}$ = ?