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

Question

asked Jul 25, 2022 30.5k views

1 Answer

John Ingle · Answer 1 · 2022-07-29T02:43:42+0000

Answer:

The values of
and
are
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 = (20)/(√(3))

b = (20√(3))/(3)

The values of
and
are
and
(20√(3))/(3) , respectively.