Question

Explain Solution of this equation!!!



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Answer 1

Question :

Solve :-

$\bf{\dfrac{\sqrt{5} + 2\sqrt{6} - \sqrt{5} - 2\sqrt{6}}{\sqrt{5} + 2\sqrt{6} + \sqrt{5} - 2\sqrt{6}}}$

To find :

The value of the given Equation.

solution :

$:\implies \bf{\dfrac{\sqrt{5} + 2\sqrt{6} - \sqrt{5} - 2\sqrt{6}}{\sqrt{5} + 2\sqrt{6} + \sqrt{5} - 2\sqrt{6}}}$

By putting the like terms together, we get :

$:\implies \bf{\dfrac{\sqrt{5} - \sqrt{5} - 2\sqrt{6} + 2\sqrt{6}}{\sqrt{5} + \sqrt{5} - 2\sqrt{6} + 2\sqrt{6}}}$

By Cancelling the equal and opposite terms , we get :

$:\implies \bf{\dfrac{\not{\sqrt{5}} - \not{\sqrt{5}} - \not{2\sqrt{6}} + \not{2\sqrt{6}}}{\sqrt{5} + \sqrt{5} - \not{2\sqrt{6}} + \not{2\sqrt{6}}}}$

$:\implies \bf{\dfrac{0}{\sqrt{5} + \sqrt{5}}}$

Now by adding the like terms in the denominator , we get :

[For example :- (a + a) = 2a]

$:\implies \bf{\dfrac{0}{2\sqrt{5}}}$

We know that anything divided by zero gives the answer is 0.

Thus by using the above identity , we get :

$:\implies \bf{0}$

Hence the value of the Equation is 0.i.e,

$\underline{\boxed{\therefore \bf{\dfrac{\sqrt{5} + 2\sqrt{6} - \sqrt{5} - 2\sqrt{6}}{\sqrt{5} + 2\sqrt{6} + \sqrt{5} - 2\sqrt{6}} = 0}}}$

Additional Information :-

Rational numbers :

What are Rational numbers ?

Rational numbers can be defined as the numbers that can written in p/q form are known as Rational numbers.

Note :-

• The denominator (q) of rational can't be equal to 0 ,i.e, q ≠ 0

• In a Rational number p and q are both Integers.

Some Properties of Rational numbers :-

• If x and y are two rational numbers then , x + y will also be a rational number.

• If x and y are two rational numbers then , x - y will also be a rational number.

• If x and y are two rational numbers then , x × y will also be a rational number.

• If x and y are two rational numbers then , x - y will also be a rational number.

$\rule{400}{2}$

Real Numbers :

What are Real Numbers ?

Real Numbers can be defined as the group of all the rational and irrational numbers.

Properties of Real Numbers :-

(The properties of Real numbers are similar to properties of Rational numbers ,i.e,)

• If x and y are two rational numbers then , x + y will also be a rational number.
• If x and y are two rational numbers then , x - y will also be a rational number.

• If x and y are two rational numbers then , x × y will also be a rational number.

• If x and y are two rational numbers then , x - t will also be a rational number.

$\rule{400}{2}$