Question

Find the value of a and b 5+3√2\5-3√2=a+b√2

Answer 1

Answer:

a=7/2 and b+=3/2

Step-by-step explanation:

(3 + sqrt(5)) / (3 - sqrt(5)) = (a + b*sqrt(5)) /1 , we have one equation of 2 fractions.

The cross product gives: (3 + sqrt(5)) = (3 - sqrt(5)) * (a + b*sqrt(5))

Getting rid of the brackets: 3 + sqrt(5) = 3a + 3b*sqrt(5) - 5b - a* sqrt(5)

3 + sqrt(5) = (3a -5b) + (3b - a)*sqrt(5) Separating the Rational from the Irrational,

we get 2 linear equations: 3 = (3a -5b) and

1 = (3b - a)

Multiplying the second equation by 3 gives: 3 = - 3a + 9b

adding the first equation: 3 = 3a -5b

we get : 3+3= - 3a + 3a + 9b - 5b

Eliminating the variable a : 6 = 4 b this gives b = 6/4 = 3/2

Now knowing b=3/2 , we substitute it in 1 = (3b - a) and we get a = 7/2

The answer is: a = 7/2 ; and b = 3/2

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Answer 2

Answer:

a = 43/7

b = 30/7

Step-by-step explanation:

$\frac{5 + 3\sqrt{2} }{5 - 3\sqrt{2} }$ = a+b$\sqrt{2}$

Rationalize the denominator :- (5 + 3$\sqrt{2}$)² / 25 -18

= 25 + 18 + 30√2 / 7

= 43 + 30√2 / 7

= 43/7 + 30√2 / 7

= a + b√2

a = 43/7

b = 30/7