Exercise 53 Page 516

Substitute 3+isqrt(2) into the given equation and then simplify.

See solution.

Practice makes perfect

We can determine whether 3+isqrt(2) is a solution by substituting it into the equation and simplifying using the order of operations. Let's do it!

x^2 - 6x + 11 = 0

x= 3 + isqrt(2)

(3+isqrt(2))^2 - 6(3+isqrt(2))+11? =0

(a+b)^2=a^2+2ab+b^2

3^2 + 2 * 3 * isqrt(2) +(isqrt(2))^2 - 6(3+isqrt(2))+11? =0

Distribute -6

3^2 + 2 * 3 * isqrt(2)+(isqrt(2))^2 - 18-6* isqrt(2)+11? =0

3^2 + 6 * isqrt(2)+(isqrt(2))^2 - 18-6* isqrt(2)+11? =0

Calculate power

9 + 6 * isqrt(2)+i^2 * 2 - 18-6* isqrt(2)+11? =0

Remember that i — the imaginary unit — equals -1 when squared.

9 + 6 * isqrt(2)+i^2 * 2 - 18-6* isqrt(2)+11? =0

i^2=- 1

9 + 6 * isqrt(2)-1 * 2 - 18-6* isqrt(2)+11? =0

9 + 6 * isqrt(2)-2 - 18-6* isqrt(2)+11? =0

Add and subtract terms

0 = 0 ✓

Since both sides are equal, 3+isqrt(2) is a solution to the equation.

10.1.1 Introduction to Arithmetic Series p.504-506

10.1.2 More Arithmetic Series p.510-511

10.1.3 General Arithmetic Series p.515-516

10.1.4 Summation Notation and Combinations of Series p.519-521

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