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zhannawk [14.2K]
3 years ago
12

If a = 4 - √15, find a^4 +1\a^4

Mathematics
1 answer:
Luden [163]3 years ago
7 0

Answer:

(\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2}  -4\\

Step-by-step explanation:

a=4-\sqrt{15}

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\\

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