Question

a^4+a^2b^2+b^4=8 what is the value of a^2+b^2​

Answer 1

the correct que is :

If a4 + a2b2 + b4 = 8 and a2 + ab + b2 = 4, then the value of ab is:

Step-by-step explanation:

Given

a4 + a2b2 + b4 = 8 ----- equation -(i)

And,

a2 + ab + b2 = 4

a2 + b2 = 4 - ab ----------------- equation -(ii)

From Equation (i)

⇒ a4 + b4 + a2b2 = 8

⇒ (a2 + b2)2 - 2a2b2 + a2b2 = 8

⇒ (4-ab)2 - a2b2 = 8

⇒ 16 -8ab + a2b2 - a2b2 = 8

⇒ -8ab = 8 - 16

∴ ab = 1

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