How do I simplify this without using a calculator?
(sqrt of 2 + 1)^5 + (sqrt of 2 - 1)^5
Please show the way...thanks.
(sqrt of 2 + 1)^5 + (sqrt of 2 - 1)^5
Please show the way...thanks.
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(sqrt of 2 + 1)^5 + (sqrt of 2 - 1)^5
= (sqrt of 2 + 1)^4 (sqrt of 2 + 1) + (sqrt of 2 - 1)^4 (sqrt of 2 - 1)
= (3 + 2 sqrt of 2)^2 (sqrt of 2 + 1) + (3 - 2 sqrt of 2)^2 (sqrt of 2 - 1)
= (17 + 12 sqrt of 2) (sqrt of 2 + 1) + (17 - 12 sqrt of 2) (sqrt of 2 - 1)
= 34 sqrt of 2 + 24 sqrt of 2
= 58 sqrt of 2
= (sqrt of 2 + 1)^4 (sqrt of 2 + 1) + (sqrt of 2 - 1)^4 (sqrt of 2 - 1)
= (3 + 2 sqrt of 2)^2 (sqrt of 2 + 1) + (3 - 2 sqrt of 2)^2 (sqrt of 2 - 1)
= (17 + 12 sqrt of 2) (sqrt of 2 + 1) + (17 - 12 sqrt of 2) (sqrt of 2 - 1)
= 34 sqrt of 2 + 24 sqrt of 2
= 58 sqrt of 2