Question

(root 2+1 upon root 2-1)-( root 2-1 upon root 2+1)

Answer 1

Answer:

2/root3

Step-by-step explanation:

(root 2+1 upon 2-1)-(root2-1 upon root 2+1)

root 2+1=root 3/2-1 - root 1 upon 3

Answer 2

ANSWER:

• The value of above expression = 4√2

GIVEN:

$\frac{ \sqrt{2} + 1}{ \sqrt{2} - 1 } - \frac{ \sqrt{2} - 1}{ \sqrt{2} + 1 }$

TO FIND:

• The value of above expression.

SOLUTION:

$= \frac{ \sqrt{2} + 1}{ \sqrt{2} - 1 } - \frac{ \sqrt{2} - 1}{ \sqrt{2} + 1 } \\ \\ = \frac{( \sqrt{2} + 1)( \sqrt{2} + 1)}{ (\sqrt{2} - 1)( \sqrt{2} + 1)} - \frac{( \sqrt{2} - 1)( \sqrt{2} - 1)}{ (\sqrt{2} + 1)( \sqrt{2} - 1)} \\ \\ = \frac{( \sqrt{2} + 1) {}^{2} }{( \sqrt{2}) {}^{2} - 1 {}^{2} } - \frac{( \sqrt{2} - 1) {}^{2} }{( \sqrt{2}) {}^{2} - 1 {}^{2} } \: \\ \\ = \frac{( \sqrt{2} ) {}^{2} + 1 {}^{2} + 2 \times \sqrt{2} \times 1 }{2 - 1} - \frac{( \sqrt{2} ) {}^{2} + 1 {}^{2} - 2 \times \sqrt{2} \times 1 }{2 - 1} \: \\ \\ = 2 + 1 + 2 \sqrt{2} - (2 + 1 - 2 \sqrt{2} ) \\ \\ = 3 + 2 \sqrt{2} - 3 + 2 \sqrt{2} \\ \\ = 4 \sqrt{2}$

The value of above expression = 4√2

NOTE:

• Firstly in rationalization we have to remove the root from the the denominator.
• In order to remove the square root from the denominator we have to multiply with numbers such that the denominator root get removed.