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Question 70
If $$a^{4}+ a^{2}b ^{2}+ b^{4}$$ =8 and $$a^{2}+ ab+ b^{2}$$ = 4, then the value of ab is
Solution
$$\left(a^2+ab+b^2\right)^2=16$$
$$a^4+a^2b^2+b^4+2.a^2.ab+2.ab.b^2+2.b^2.a^2=16$$
$$8+2ab\left(a^2+b^2+ab\right)=16$$
2ab(4) = 16-8
8ab = 8
ab = 1
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