If a4+a2b2+b4=3 and a2+ab+b2=3, what is the value of a2+b2?
Solution
Correct Answer: Option D
দেওয়া আছে, a4+a2b2+b4=3 .........(i)
From (2) + (3),
2 (a2 + b2)=4
∴ a2 + b2=2
এবং a2+ab+b2=3 .............(ii)
এখন, (i) নং হতে পাই, a4+a2b2+b4=3
⇒ (a2)2 + 2a2b2 + (b2)2 - a2b2 = 3
⇒ (a2 + b2 )2 - a2b2 = 3
⇒ (a2 + b2 )2 - (ab)2 = 3
⇒ (a2 + b2 + ab) (a2 + b2 - ab) = 3
⇒ 3.(a2 + b2 - ab) = 3 [From 2]
⇒ a2 + b2 - ab = 1 -----(3)
From (2) + (3),
2 (a2 + b2)=4
∴ a2 + b2=2
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