IDNLearn.com offers a unique blend of expert answers and community-driven insights. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.
Answer:
[tex](\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\[/tex]
Step-by-step explanation:
[tex]a=4-\sqrt{15}[/tex]
[tex]a^{4} +\frac{1}{a^{4} }\\=a^{2^{2} } +\frac{1}{a^{2^{2} } }\\\\=(x^{2} +\frac{1}{a^{2} } )^{2} -2a^{2} \frac{1}{a^{2} } \\=(a +\frac{1}{a } )^{2} -2a \frac{1}{a}-2\\=(4-\sqrt{15} +\frac{1}{4-\sqrt{15} }) ^{2} -4\\\=(\frac{16-15-4+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\=(\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\[/tex]