Question

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

Answer 1

ANSWER:

value of "a" is: a= -b√3+7+4√3

value of "b" is:  $\frac{-a\sqrt{3}+7\sqrt{3} }{y} +4$

STEP-BY-STEP EXPLANATION:

how to get the value of "a":

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)

-a + 7 + 4√3 = b√3  ⇔ -a = b√3 -7 - 4√3

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

a = -b√3 + 7 + 4√3

how to get the value of "b":

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

(2 + $\sqrt{3}$) × (2 + $\sqrt{3}$ ) = a + b$\sqrt{3}$   →  (2 + $\sqrt{3}$) × (2 +$\sqrt{3}$ ) = a + $\sqrt{3}$b

2. (write the repeated multiplication in exponential form)

(2 + √3)² =a + $\sqrt{3}$b

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

4 + 4$\sqrt{3}$ + 3 = a + $\sqrt{3}$b

4. (add the numbers)

7 + 4 $\sqrt{3}$ = a + $\sqrt{3}$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)

- $\sqrt{3}$b + 7  + 4 $\sqrt{3}$ = a  → -$\sqrt{3}$b = a - 7 - 4$\sqrt{3}$

6. (divide both sides of the equation by $-\sqrt{3}$)  

b = $- \frac{a}{\sqrt{3} } + \frac{7}{\sqrt{3}} + 4$

7. (rationalize the denominator)

b = $b=-\frac{a\sqrt{3} }{\s3}} +\frac{7\sqrt{3} }{{3} } +4$

8. (write all numerators above the common denominator)

b =  $\frac{-a\sqrt{3}+7\sqrt{3} }{y} +4$

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