If a and b satisfy 3a 2+5 | b | = 7. S = 2a 2-3 | b |, what is the range of S? This question is extremely BT, so I attach the answer (I have been doing it all day). ∫3a 2+5 | b | = 7∴5 | b | = 7-3a 2 | b | = 7/5-3/5a 2。

①∵a^2≥0

|b|≥0∴a^2≥0

7/5-3/5a 2≥0:0≤a2≤7/3∶s = 2a 2-3 | b |

② Substitute ① into ②, where s = 2a2-3 (7/5-3/5a2) =19/5a21/5 and ∵ 0 ≤ A 2 ≤ 7/3 ∴ 0 ≤19. 5 when 19/5A 2 is133/15:133/15-215 =14/2 ∴.