I'll mark as brainliest if you get the correct answer WITH step by step explaination.​

ANSWER:

value of "a" is: a= -b√3+7+4√3

value of "b" is:  

STEP-BY-STEP EXPLANATION:

1. (rationalize the denominator)

(2 + √3) × (2 + √3) =a + b√3

2. (write the repeated multiplication in exponential form)

(2 + √3)² =a + b√3

3. (use (a + b)² = a² + 2ab + b²  to expand the expression)

4 + 4√3 + 3 = a + b√3

4. ( add the numbers)

7 + 4√3 = a + b√3

5. (move the variable to the left-hand side and change its sign. then, move the constants to the right-hand side and change their signs)

6. (change the signs on both sides of the equation)

a = -b√3 + 7 + 4√3

1. (rationalize the denominator. then, use the commutative property to reorder the terms)

(2 + ) × (2 + ) = a + b   →  (2 + ) × (2 + ) = a + b

2. (write the repeated multiplication in exponential form)

(2 + √3)² =a + b

3. (use (a + b)² = a² + 2ab + b²  to expand the expression)

4 + 4 + 3 = a + b

4. (add the numbers)

7 + 4 = a + b

5. (move the expression to the left-hand side and change its sign. then, move the constants to the right-hand side and change their signs)

- b + 7  + 4 = a  → -b = a - 7 - 4

6. (divide both sides of the equation by )  

b =

7. (rationalize the denominator)

b =

8. (write all numerators above the common denominator)

b =  

there you go! I hope this helped. goodluck! :)

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