Question

(2-√5)+ (2+√5)=?? please explain step by step ​

Answer 1

Solution :-

Given :- (2-√5)+ (2+√5)

We have to simplify

Lets do step by step

Step:- 1

First write the given question

(2-√5)+ (2+√5)

Step :- 2

Open the brackets

(2-√5)+ (2+√5)

2 - √5 + 2 + √5

Step : 3

Keep like terms a side

2 + 2 -√5 + √5

Step :- 4

What we got simplify expression

4 - √5 + √5

4 +$\sqrt{ \not{5}}-{\sqrt{ \not{5}}}$

4

So, the value of (2-√5)+ (2+√5)= 4

Answer 2

Answer:

The only clear way to solve it successfully is by making the two fractions’ denominators one. And the easy way to do that in your case to multiply the first by 2+√5 and the second by 2-√5. So, you obtain:

(2+√5/2-√5) + (2-√5/2+√5)= ((2+√5)*(2+√5)/(2-√5)*(2+√5)) + ((2-√5)*(2-√5)/(2+√5)*(2-√5))= ((2+√5)²+(2-√5)²)/((2+√5)*(2-√5))=((4+5+4√5)+(4+5–4√5))/(2²-√5²)=(9+9+4√5–4√5)/(4–5)=18/(-1)=-18

The mathematical properties used:

(a+b)²=a²+2ab+b² , (a-b)²=a²-2ab+b² and (a+b)*(a-b)=a²-b²