Question

If x= 2(√2+√6)/3√(2+√3), then x is equal to-- a)4/3 b)16/9 c)2/3 d)3/4

Answer 1

x=2 (root2+root6)/3root (2+root3)

3x.root (2+root3)= 2 (root2+root6)
take square both side
9x^2. (2+root3) =4 (root2+root6)^2
9x^2 (2+root3)=4 (8+4root3)
9x^2 (2+root3)=16 (2+root3)
9x^2 = 16
x^2 =16/9
take square root both side
x=+_4/3
hence option (a) is correct .

Answer 2

Step-by-step explanation:

X=2(√2+√6)/3(√2+√3)

3X(√2+√3)=2(√2+√6)

squaring both sides

9X²(2+√3)=4(8+4√3)

9X²(2+√3)=16(2+√3)

(2+√3) is on both side, that's why it is canceled

then we get,

9X²=16

X²=16/9

(X)²=(16/9)²

X=4/3

So, last option is correct