Math, asked by itsalanlewis, 3 days ago

The value of a+b root 7 + root 5/root 7-root 5=a+b root 5

Answers

Answered by tennetiraj86
5

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 = +2ab+

(a+b)(a-b) = -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+135 = 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

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