Use the fact that is a solution of x⁴

Question

Use the fact that is a solution of x⁴ - 2 = 0 to approximate with an error of at most 0.005. A) 1.169 B) 1.179 C) 1.189 D) 1.199 E) 1.209

Quizplus · Accepted Answer

We can use the fact that 11ead0bc_8e83_e9c2_99a0_4b72a0e2f7d2_TB6988_11 is a solution of x⁴ - 2 = 0 to find an approximation for 11ead0bc_8e84_10d3_99a0_6d98660c1b31_TB6988_11. Let a be the decimal approximation of 11ead0bc_8e83_e9c2_99a0_4b72a0e2f7d2_TB6988_11 with an error of at most 0.005. Then we have: a⁴ - 2 = 0 +- 0.005 Adding 2 to both sides and using the fact that ⁴ = 2^(52), we get: a = 2/(2^(52)) +- 0.005 Simplifying, we get: a = 1.179 +- 0.005 Therefore, the best choice is B, 1.179.

Use the Fact That Is a Solution of X4