Question

find the value of a and b in each of the following 2-√5/2+√5 =a√5+b

correct answer only ​

Answer 1

Answer:

$a = \frac{1}{2}$

$b = 2$

Step-by-step explanation:

Given :

$2 - \frac{ \sqrt{5} }{2} + \sqrt{5} = a \sqrt{5} + b$

To find :

The value of a and b.

Solution :

$\frac{2}{1} - \frac{ \sqrt{5} }{2} + \frac{ \sqrt{5} }{1} = a \sqrt{5} + b$

$\frac{4 - \sqrt{5} + 2 \sqrt{5} }{2} = a \sqrt{5} + b$

$\frac{4 + \sqrt{5} }{2} = a \sqrt{5} + b$

$\frac{4}{2} + \frac{ \sqrt{5} }{2} = a \sqrt{5} + b$

$2 + \frac{ \sqrt{5} }{2} = a \sqrt{5} + b$

$\frac{1 \sqrt{5} }{2} + 2 = a \sqrt{5} + b$

$a = \frac{1}{2}$

$b = 2$

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Answer 2

Step-by-step explanation:

(2-√5)/(2+√5) = a√5 + b

=> (2-√5)²/(2+√5)(2-√5) = a√5 +b

=> (2-√5)²/(2²-√5²) = a√5 + b

=> (4-4√5+5)/(-1) = a√5 + b

=> -9 + 4√5 = b + a√5

comparing both sides , b= -9, a= 4