ANSWER:
value of "a" is: a= -b√3+7+4√3
value of "b" is:
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 + ) × (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! :)