Question

Left parenthesis 5 plus 2 square root of 6 right parenthesis squared = a plus b square root of 6 then the value of a and b are

Answer 1

The values of
`a` and
`b` are
`33` and
`(20√(3))/(3)`, respectively.

Explanation:

The statement is equivalent to the following mathematic expression:

`\left(5 + 2√(2))^(2) = a + b\cdot √(6)` (1)

By definition of the perfect square trinomial:

`25 + 20\cdot √(2) + 8 = a + b\cdot √(6)`

`33 + 20√(2) = a + b\cdot √(6)`

And by direct comparison we have the following system:

`a = 33` (2)

`b\cdot √(6) = 20√(2)` (3)

By (3), we solve for
`b`:

`b = (20)/(√(3))`

`b = (20√(3))/(3)`

The values of
`a` and
`b` are
`33` and
`(20√(3))/(3)`, respectively.