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2

Part of 2018 CMI B.Sc. Entrance Exam

Problems(1)

CMI 2018 #2

Source: Chennai Mathematical Institute

8/30/2018
Answer the following questions :
<spanclass=′latex−bold′>(a)</span><span class='latex-bold'>(a)</span> Find all real solutions of the equation (x2−2x)x2+x−6=1\Big(x^2-2x\Big)^{x^2+x-6}=1 Explain why your solutions are the only solutions.
<spanclass=′latex−bold′>(b)</span><span class='latex-bold'>(b)</span> The following expression is a rational number. Find its value. 63+103−63−103\sqrt[3]{6\sqrt{3}+10} -\sqrt[3]{6\sqrt{3}-10}
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