(sqrt3-1)/(sqrt3+1)=a+bsqrt3
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45
Solution :
_____________________________________________________________
Given :
a & b both are rational numbers.
_____________________________________________________________
To Find :
a possible values for a & b
_____________________________________________________________
We can find a possible value by,
⇒ Rationalizing the denominator,.
By using the principle (only for integers in square root) :
(a - b) (a + b) = a² - b² , => in denominator (To bring them to standard form)
Here the denominator :
⇒ √3 + 1 is in the form a + b
So, Multiplying both numerator & denominator by √3 - 1,. as (a - b)
We will get the form (a + b)(a - b)
⇒ By this way we can find values easily,.
The steps are as Follows :
⇒
⇒
The numerator is of the form :
(a - b)²,.
Hence,.
We know that,.
(a - b)² = a² - 2ab + b²
By substituting the values ,
We get,.
⇒
⇒
⇒
⇒
⇒ 2 - √3
________________
It is of the form a + b√3
Hence,.
if a = 2 & b = -1,.
⇒ 2 + (-1)√3
⇒ 2 - √3
∴ a = 2,
∴ b = -1
_____________________________________________________________
Hope it Helps !!
⇒ Mark as Brainliest,.(if possible)
_____________________________________________________________
Given :
a & b both are rational numbers.
_____________________________________________________________
To Find :
a possible values for a & b
_____________________________________________________________
We can find a possible value by,
⇒ Rationalizing the denominator,.
By using the principle (only for integers in square root) :
(a - b) (a + b) = a² - b² , => in denominator (To bring them to standard form)
Here the denominator :
⇒ √3 + 1 is in the form a + b
So, Multiplying both numerator & denominator by √3 - 1,. as (a - b)
We will get the form (a + b)(a - b)
⇒ By this way we can find values easily,.
The steps are as Follows :
⇒
⇒
The numerator is of the form :
(a - b)²,.
Hence,.
We know that,.
(a - b)² = a² - 2ab + b²
By substituting the values ,
We get,.
⇒
⇒
⇒
⇒
⇒ 2 - √3
________________
It is of the form a + b√3
Hence,.
if a = 2 & b = -1,.
⇒ 2 + (-1)√3
⇒ 2 - √3
∴ a = 2,
∴ b = -1
_____________________________________________________________
Hope it Helps !!
⇒ Mark as Brainliest,.(if possible)
Bhumikbnkc:
very very thanks
Answered by
28
Hey friend,
Here is the answer you were looking for:

Hope this helps!!!
@Mahak24
Thanks...
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Here is the answer you were looking for:
Hope this helps!!!
@Mahak24
Thanks...
☺☺
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