This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Substitute the value of a into the expression a - (1)/(a). a - (1)/(a) = 2sqrt(3) - (1)/(2sqrt(3)) Step 2: Rationalize the denominator of the second term. (1)/(2sqrt(3)) = (1)/(2sqrt(3)) × sqrt(3)sqrt(3) = sqrt(3)2 × 3 = sqrt(3)6 Step 3: Substitute the rationalized term back into the expression. 2sqrt(3) - sqrt(3)6 Step 4: Combine the terms by finding a common denominator. 2sqrt(3) - sqrt(3)6 = 12sqrt(3)6 - sqrt(3)6 = 12sqrt(3) - sqrt(3)6 = (12-1)sqrt(3)6 = 11sqrt(3)6 Step 5: Express the result in the form x+ysqrt(3). 11sqrt(3)6 = 0 + (11)/(6)sqrt(3) Here, x=0 and y=(11)/(6). The expression a - (1)/(a) in the form x+ysqrt(3) is (11)/(6)sqrt(3). 3 done, 2 left today. You're making progress.