√5-2 - √5+2
____ ____. =
√5+2 √√5-2
Answers
Answer:
Option (B)
Step-by-step explanation:
Solution :-
Given that :
[(√5-2)/(√5+2)] - [(√5+2)/(√5-2)]
On taking first part in that
[(√5-2)/(√5+2)]
The denominator = √5+2
Rationalising factor of √5+2 is √5-2
On Rationalising the denominator then
=> [(√5-2)/(√5+2)] × [(√5-2)/(√5-2)]
=> [(√5-2)(√5-2)/(√5+2)(√5-2)]
=> (√5-2)²/[(√5+2)/(√5-2)]
=> (√5-2)²/[(√5)²-2²]
Since (a+b)(a-b) = a²-b²
Where , a = √5 and b = 2
=> (√5-2)²/(5-4)
=> (√5-2)²/1
=> (√5-2)²
It is in the form of (a-b)²
Where, a = √5 and b = 2
(a-b)² = a²-2ab+b²
=> (√5)²-2(√5)(2)+(2)²
=> 5-4√5+4
=> 9-4√5
[(√5-2)/(√5+2)] = 9-4√5 -----------------(1)
On taking the second part then
[(√5+2)/(√5-2)]
The denominator = √5-2
Rationalising factor of √5-2 is √5+2
On Rationalising the denominator then
=> [(√5+2)/(√5-2)] × [(√5+2)/(√5+2)]
=> [(√5+2)(√5+2)/(√5-2)(√5+2)]
=> (√5+2)²/[(√5+2)/(√5-2)]
=> (√5+2)²/[(√5)²-2²]
Since (a+b)(a-b) = a²-b²
Where , a = √5 and b = 2
=> (√5+2)²/(5-4)
=> (√5+2)²/1
=> (√5+2)²
It is in the form of (a+b)²
Where, a = √5 and b = 2
(a+b)² = a²+2ab+b²
=> (√5)²+2(√5)(2)+(2)²
=> 5+4√5+4
=> 9+4√5
[(√5+2)/(√5-2)] = 9+4√5 -----------------(2)
Now,
[(√5-2)/(√5+2)] - [(√5+2)/(√5-2)]
From (1)&(2)
=> (9-4√5)-(9+4√5)
=> 9-4√5-9-4√5
=> (9-9)-(4√5+4√5)
=> 0-(8√5)
=> -8√5
Answer :-
The value of [(√5-2)/(√5+2)] - [(√5+2)/(√5-2)] is -8√5
Used formulae:-
- (a+b)² = a²+2ab+b²
- (a-b)² = a²-2ab+b²
- (a+b)(a-b) = a²-b²
- The Rationalising factor of √a+b is √a-b
- The Rationalising factor of √a-b is √a+b
Answer:
8{5
Step-by-step explanation:
oh no my mind its broken