Question

1+root2/(3-root2)^2 can be writen in the form a+b root2

find the values of a and the value of b

Answer 1

We can start by multiplying the denominator by its conjugate:

(3 - root2)^2 = (3 - root2)(3 + root2) = 9 - 2*root2^2 = 9 - 2 = 7

Now, we can divide the numerator by the denominator:

1+root2/(3-root2)^2 = (1+root2)/7

To get the expression in the form a + b*root2, we can see that a = 1/7 and b = 1/7 *root2

So the final form of the expression is:

1/7 + 1/7 *root2

a = 1/7 and b = 1/7 *root2

Explanation: