Step 1: l ki value nikalna
Expansion: (2x5/2−xl4)9
General term Tr+1 ka formula:
Tr+1=(r9)(2x5/2)9−r(−4x−l)r
Tr+1=(r9)(21)9−r(−4)r⋅x25(9−r)−lr
Constant term ke liye x ki power 0 honi chahiye:
Humein diya gaya hai ki constant term −84 hai. Constant term tabhi negative ho sakti hai jab r ek odd number ho (kyunki (−4)r hai).
Agar hum r=3 rakhte hain:
Term=(39)(21)6(−4)3=84⋅641⋅(−64)=−84
Ye match kar raha hai! Iska matlab r=3 hai.
Ab r=3 ko power waali equation mein rakhte hain:
25(9−3)−3l=0⟹25(6)=3l⟹15=3l⟹l=5
Step 2: x−3l ka coefficient nikalna
Humein x−3l=x−15 ka coefficient chahiye. Power equation use karte hain:
245−5r−10r=−15⟹45−15r=−30⟹15r=75⟹r=5
Ab r=5 ke liye coefficient nikalte hain:
Coeff=(59)(21)9−5(−4)5=126⋅241⋅(−210)
Coeff=126⋅(−26)=126⋅(−64)=−8064
Humein isse 2αβ ki form mein likhna hai jahan β odd ho:
−8064=−126×64=−(63×2)×26=−63×27
Yahan α=7 aur β=−63 (jo ki odd hai aur < 0 hai).
Step 3: Final Answer
Humein nikalna hai ∣αl−β∣:
Answer: 98
