A) 4
B) 5
C) 6
D) 8
Correct Answer: C
Solution :
\[\alpha +\beta =1154\] and \[\alpha \beta =1\] |
\[{{(\sqrt{\alpha }+\sqrt{\beta })}^{2}}=\alpha +\beta +2\sqrt{\alpha \beta }\] |
\[=1154+2=1156={{(34)}^{2}}\] |
\[\sqrt{\alpha }+\sqrt{\beta }=34\] |
Again, \[{{({{\alpha }^{1/4}}+{{\beta }^{1/4}})}^{2}}=\sqrt{\alpha }+\sqrt{\beta }+2{{(\alpha \beta )}^{1/4}}\] |
\[=34+2=36\] |
\[{{\alpha }^{1/4}}+{{\beta }^{1/4}}=6\] |
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