Advertisement Remove all ads

# If √ 3 − 1 √ 3 + 1 = X + Y √ 3 , Find the Values of X and Y. - Mathematics

Answer in Brief

If$\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},$  find the values of and y.

Advertisement Remove all ads

#### Solution

It is given that;

.  (sqrt3-1)/ (sqrt3+1 )= x+ysqrt3  we need to find x and y

We know that rationalization factor for  sqrt3 +1 issqrt3 -1 . We will multiply numerator and denominator of the given expression (sqrt3-1)/(sqrt3+1)by,sqrt3-1 to get

(sqrt3-1)/ (sqrt3+1 ) xx (sqrt3-1)/(sqrt3-1) = ((sqrt3)^2 + (1) ^2 - 2 xx sqrt3 xx1) /((sqrt3)^2 - (1)^2)

= (3+1-2sqrt3) /(3-1)

 = (4-2sqrt3)/2

 = 2-sqrt3

On equating rational and irrational terms, we get

 x + y sqrt3 = 2-sqrt3

Hence, we get  x= 2, y = -1

Is there an error in this question or solution?
Advertisement Remove all ads

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Q 4 | Page 16
Advertisement Remove all ads

#### Video TutorialsVIEW ALL 

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?
Course