-37
No. 30 x 7-3 = 120 27 x 7 = 189
Let the numbers be x and y, then x + y = 60 (which yields y = 60 - x) xy = 1600 (replace y with 60 - x) x(60 - x) = 1600 60x - x2 = 1600 (multiply by -1 to both sides) x2 - 60x = -1600 (add 302 to both sides to complete the square) x2 - 60x + 302 = -1600 + 900 (x - 30)2 = -700 (take the square root of both sides) x - 30 = ± √-700 (add 30 to both sides and write -700 = (100)(7)(-1)) x = 30 ± (√100)(√7)(√-1) x = 30 ± (10√7)i So, x = 30 + (10√7)i or x = 30 - (10√7)i thus, y = 60 - [30 + (10√7)i] or y = 60 - [30 - (10√7)i ] y = 30 - (10√7)i or y = 30 + (10√7)i Therefore, [30 + (10√7)i] + [30 - (10√7)i] = 60 [30 + (10√7)i] [30 - (10√7)i] = 1600 Check:
Example: 1/30 and 1/42Factor the denominators.2 x 3 x 5 = 302 x 3 x 7 = 42Combine the factors, eliminating duplicates.2 x 3 x 5 x 7 = 210, the LCDConvert each fraction by multiplying by what's missing.30 x 7 = 21042 x 5 = 2101/30 x 7/7 = 7/2101/42 x 5/5 = 5/210
2730
2 x 7 = 14 3 x 7 = 21 2 x 3 x 5 = 30
30 (30 x 7, 30 x 15)
592 6 x 7 = 42 6 x 30 = 180 10 x 7 = 70 10 x 30 = 300 Total: 592
210. 30 = 2 x 3 x 5 21 = 3 x 7 lcm = 2 x 3 x 5 x 7 = 210
2 x 7 = 14 2 x 3 x 5 = 30 2 x 3 x 5 x 7 = 210, the LCM
70 x 30 = 2100 7 x 30 = 210
2 x 3 x 5 x 7 2 x 3 = 6 6 x 5 = 30 30 x 7 = 210 2 x 3 x 5 x 7 = 210