1. Dono equations ko equate karo:
Chunki dono 100 ke barabar hain:
2. Saari terms ek side le aao:
3. Formula mein set karo:
(a2−2ab+b2) ko (a−b)2 likh sakte hain:
Isko balance karne ke liye dono taraf b2 add karo:
4. Pythagorean Triplet check karo:
Hume pata hai 32+42=52.
Maano b=5:
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(a−b)=3⟹a−5=3⟹a=8
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(c−b)=4⟹c−5=4⟹c=9
Ab ye values original equation mein check karo:
2ab−c2=2(8)(5)−92=80−81=−1 (Hume 100 chahiye, so ye triplet fit nahi hai).
5. Shortcut Method (Adding Equations):
Dono equations ko add kar do:
(a2+2ab+b2)−(c2+2bc)=100+100
Ab options se value try karo. Agar ca+b=2 (Option c) rakhein:
Toh a+b=2c. Isse equation mein put karo:
Agar c=10 aur b=5 lein:
3(100)−2(5)(10)=300−100=200
Ye perfectly match kar raha hai!
Conclusion:
Jab c=10,b=5 aur a=15, toh ca+b=1015+5=2.
Correct Option: (c) 2
