Вправи 1001 - 1100 » 1010 (б)

б) ((6a+ b)/(2a-3b))2 – 4((6a+ b)/(2a-3b)) = 5; (6a+ b)/(2a-3b) = t, t ≠ 0; t2 – 4t = 5; t2 – 4t – 5 = 0; D = (–4)2 – 4 • 1 • (–5) = 16 + 20 = 36 = 62; t1 = (4-6)/2 = (-2)/2 = –1; t2 = (4+6)/2 = 10/2 = 5. (6a+ b)/(2a-3b) = –1; (6a+ b)/(2a-3b) = 5; 6a + b = –2a + 3b; 6a + b = 10a – 15b; 6a + 2a = 3b – b; 6a – 10a = –15b – b; 8a = 2b (: 8); –4а = –16b (:(–4); а = b/4; а = 4b. Відповідь: а = b/4 або а = 4b.