Question

if (4+root 5)/(4-root5)=a+b*root5 find a and b

Answer 1

Answer:

a = 4root5 b = 5

Step-by-step explanation:

4 + root5 ÷ 4 - root5 = (a + b) root5

(4 + root5)(4 + root5) ÷ 16 - 5 = (a + b)root5

16 + 4roo5 + 4root5 + 5 = (a+b) root5

21 + 40 ÷ 11 = (a + b)root5

51/11root5 - b = a

51 - 11root5 b / 11root5 = a

Answer 2

Answer:

a= -21 and b = -8

Step-by-step explanation:

solve left hand side

(4 + √5)/ (4-√5)

rationalising

(4+√5)÷(4-√5) *(4+√5)/(4+√5)

(4+√5)^2/(4)^2 -(√5)^2

(4)^2 +(√5)^2+ 2(4)(√5)/4-5

16+5+8√5 / -1

subtraction singh in denominator will go to numerator

-( 21+8√5)

now take left hand side equal to right hand side

-21-8√5 = a+b *√5

therefore ,

a=-21 ,b = -8

√5 will be cancelled out

hope this would be helpful to you