Find the sum of all real x for which (x² − 5x + 5)^(x² − 9x + 20) = 1.

Question

Accepted Answer

15. Three ways: base 1 (x² − 5x + 4 = 0: x = 1, 4); exponent 0 with non-zero base (x² − 9x + 20 = 0: x = 4, 5); base −1 with an even exponent (x² − 5x + 6 = 0: x = 2 gives exponent 6, x = 3 gives 2 — both even). Solutions 1, 2, 3, 4, 5; sum 15.

Find the sum of all real $x$ for which $(x^{2} - 5 x + 5)^{x^{2} - 9 x + 20} = 1$ .

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Find the sum of all real x for which (x2−5x+5)x2−9x+20=1.

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

Find the sum of all real $x$ for which $(x^{2} - 5 x + 5)^{x^{2} - 9 x + 20} = 1$ .