Question

find the value of a and b if 5+√3÷√5-√3=1/2a+3b√15​

Answer 1

Answer:

the answer is = 7/2 and b = 3/2

Answer 2

Step-by-step explanation:

Given:-

find the value of a and b if

5+√3÷√5-√3=1/2a+3b√15

Correction:-

√5+√3÷√5-√3=1/2a+3b√15

To find:-

Find the values of a and b ?

Solution:-

Given that

√5+√3÷√5-√3=1/2a+3b√15

LHS = 5+√3÷√5-√3

=>( 5+√3)/(√5-√3)

Denominator = √5-√3

We know that

The Rationalising factor of√a-√b = √a+√b

Rationalising factor of √5-√3 = √5+√3

On Rationalising the denominator then

=> ( 5+√3)(√5+√3)/(√5-√3)(√5+√3)

=> (√5+√)3^2/(√5-√3)(√5+√3)

=>[(√5)^2+2(√5)(√3)+(√3)^2] /[(√5)^2-(√3)^2]

(Since (a+b)^2 =a^2+2ab+b^2 and

(a+b)(a-b)=a^2-b^2)

=> (5+2√15+3)/(5-3)

=> (8+2√15)/2

=> 2(4+√15)/2

=> 4+√15

Now ,

4+√15 = 1/2a+3b√15

=> (8/2)+ (3/3)√15 = 1/2a+3b√15

=> 8(1/2)a +3 (1/3)√15 = 1/2a+3b√15

On Comparing both sides then

a = 8 and b = 1/3

Answer:-

The value of a = 8

The value of b = 1/3

Used formulae:-

• (a+b)^2 =a^2+2ab+b^2

• (a+b)(a-b)=a^2-b^2

• The Rationalising factor of√a-√b = √a+√b