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quadratic ^ quadratic (Posted on 2021-04-06)

Please find all real solutions to the following equation:

(x^2-11*x+29)^(x^2-17*x+72) = 1

Adapted from a problem by Presh Talwalkar.

See The Solution Submitted by Larry

Rating: 4.0000 (2 votes)

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Puzzle Solution

Comment 5 of 5 |

(-1)^0 =1

1^0=1

Hence,

Either, x^2-11x+29=-1 => x^2-11 x+30 =0=> (x-6)(x-5)=0=> x=5, 6

Or, x^2-17x+72 =0=> (x-8)(x-9) = 0=> x=8,9

Or, x^2-11x+29 = 1=> x^2 -11x +28 = 0=> (x-7)(x-4)=0=> x= 4,7

Therefore, x(- {4,5,6,7,8,9}

Edited on January 9, 2024, 12:10 pm

Posted by K Sengupta on 2024-01-09 12:08:25

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