Question

find the value of a and b if 2-root5 divided by 2+root5=root5 a+b

Answer 1

Answer:

Step-by-step explanation:

# 2 - root 5 / 2 +root 5 = root 5 a + b

# 2 - root 5 * 2 - root 5 / 2 + root 5 * 2 - root 5 = root 5 a + b [ rationalising the denominator]

# ( 2 - root 5)^2/ 4 - 5 = root 5 a + b [ algebra identities]

# 4 - 4 root 5 + 5 / -1 = root 5 a + b

# -(9 - 4 root 5) / 1 = root 5 a + b

# - 9 + 4 root 5 = root 5 a + b

so,

a = 4

and b = -9