যদি a4+a2b2+b4=3 এবং a2+ab+b2=3 হয় তবে a2+b2 এর মান কত?
Solution
Correct Answer: Option A
a4+a2b2+b4=3
or,(a2)2 +2a2b2+(b2)2 -a2b2=3
or,(a2+b2)2 -(ab)2=3
or,(a2+ab+b2)(a2-ab+b2)=3
or,3=3(a2-ab+b2)
or,a2-ab+b2=1 -----(1)
আবার, a2+ab+b2=3 ---(2)
(1)+(2) যোগ করে পাই,
2(a2+b2)=4
a2+b2=2
or,(a2)2 +2a2b2+(b2)2 -a2b2=3
or,(a2+b2)2 -(ab)2=3
or,(a2+ab+b2)(a2-ab+b2)=3
or,3=3(a2-ab+b2)
or,a2-ab+b2=1 -----(1)
আবার, a2+ab+b2=3 ---(2)
(1)+(2) যোগ করে পাই,
2(a2+b2)=4
a2+b2=2
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