A) \[-1~\]
B) \[0\]
C) \[2\]
D) \[1\]
Correct Answer: D
Solution :
[d] Given equations are \[{{a}^{4}}+{{a}^{2}}{{b}^{2}}+{{b}^{4}}=8\] (ii) \[{{a}^{2}}+ab+{{b}^{2}}=4\] (ii) Squaring Eq. (ii), we get \[{{({{a}^{2}}+ab+{{b}^{2}})}^{2}}={{(4)}^{2}}\] \[{{a}^{4}}+{{a}^{2}}{{b}^{2}}+{{b}^{4}}+2{{a}^{3}}b+2a{{b}^{3}}\] \[+2{{a}^{2}}{{b}^{2}}=16\] \[\Rightarrow \] \[8+2ab({{a}^{2}}+{{b}^{2}}+ab)=16\][using Eq.(i)] \[\Rightarrow \] \[2ab({{a}^{2}}+{{b}^{2}}+ab)=8\] \[\Rightarrow \] \[2ab\times 4=8\] [using Eq. (ii)] \[\Rightarrow \] \[ab=1\] |
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