Question

please give an answer Rationalise the denominator and find the values of a and b. 7−4√3/7+4√3 = a + b √3

Answer 1

a = 97, b = - 56

Explanation:

Answer 2

a = 97, b = - 56

Explanation:

Given

`(7-4√(3) )/(7+4√(3) )`

To rationalise multiply numerator/ denominator by the conjugate of the denominator.

The conjugate of 7 + 4
`√(3)` is 7 - 4
`√(3)`

=
`((7-4√(3))(7-4√(3)) )/((7+4√(3))(7-4√(3)) )` ← expand numerator/ denominator using FOIL

=
`(49-28√(3)-28√(3)-48 )/(49-48)`

=
`(97-56√(3) )/(1)`

= 97 - 56
`√(3)`

with a = 97 and b = - 56