The value of a+b root 7 + root 5/root 7-root 5=a+b root 5
Answers
Step-by-step explanation:
Corrected Question :-
If (√7+√5)/(√7-√5) = a+b√35 then find the value of a+b ?
Given :-
(√7+√5)/(√7-√5) = a+b√35
To find :-
The value of a+b
Solution :-
Given that
(√7+√5)/(√7-√5) = a+b√35
On taking LHS : (√7+√5)/(√7-√5)
The denominator = √7-√5
We know that
The rationalising factor of √a-√b is √a+√b
The rationalising factor of √7-√5 is √7+√5
On rationalising the denominator then
=> [ (√7+√5)/(√7-√5) ]/ [√7+√5)/(√7+√5) ]
=> [ (√7+√5)(√7+√5) ]/[(√7-√5)(√7+√5) ]
=> (√7+√5)²/[(√7-√5) (√7+√5)]
=> [(√7)²+2(√7)(√5)+(√5)²]/[(√7)²-(√5)²]
Since, (a+b)² = a²+2ab+b²
(a+b)(a-b) = a²-b²
Where, a = √7 and b = √5
=> (7+2√35+5)/(7-5)
=> (12+2√35)/2
=> 2(6+√35)/2
=> 6+√35
Therefore, (√7+√5)/(√7-√5) = 6+√35
Now,
The given equation becomes
=> 6+√35 = a+b√35
=> 6+1√35 = a+b√35
On comparing both sides then
a = 6
b = 1
Now, the value of a+b = 6+1 = 7
Answer:-
The value of a+b for the given problem is 7
Used formulae:-
→ (a+b)² = a²+2ab+b²
→ (a+b)(a-b) = a²-b²
→ The rationalising factor of √a-√b is √a+√b