First, let's simplify the expression step by step:
(2-√3)^2= (2-√3)(2-√3)= 22 + 2(-√3) - √32 - √3(-√3)= 4 - 2√3 - 2√3 + 3= 7 - 4√3
(7+4√3)= 7 + 4√3
3√12 1/4= 3√3 1= 3√3
Now, substitute the values back into the expression:
(7 - 4√3)*(7 + 4√3) + 3√3= 49 - 28√3 + 28√3 - 48 (using the difference of squares formula: (a-b)(a+b) = a^2 - b^2)= 1
First, let's simplify the expression step by step:
(2-√3)^2
= (2-√3)(2-√3)
= 22 + 2(-√3) - √32 - √3(-√3)
= 4 - 2√3 - 2√3 + 3
= 7 - 4√3
(7+4√3)
= 7 + 4√3
3√12 1/4
= 3√3 1
= 3√3
Now, substitute the values back into the expression:
(7 - 4√3)*(7 + 4√3) + 3√3
= 49 - 28√3 + 28√3 - 48 (using the difference of squares formula: (a-b)(a+b) = a^2 - b^2)
= 1