What are the solutions to the equation (x^2-3x+2)^7=(x-6x+5)^7 ?

The solutions to the equation (x^2-3x+2)^7=(x-6x+5)^7 are x=1,x=-3

Find the zeros of (x^2-3x+2)^7=(x-6x+5)^7

The zeros of (x^2-3x+2)^7=(x-6x+5)^7 are x=1,x=-3

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(x^{2} - 3 x + 2)^{7} = (x - 6 x + 5)^{7}

x = 1, x = - 3

Solution steps

(x^{2} - 3 x + 2)^{7} = (x - 6 x + 5)^{7}

Expand

(x^{2} - 3 x + 2)^{7} : x^{14} - 21 x^{13} + 203 x^{12} - 1197 x^{11} + 4809 x^{10} - 13923 x^{9} + 29953 x^{8} - 48639 x^{7} + 59906 x^{6} - 55692 x^{5} + 38472 x^{4} - 19152 x^{3} + 6496 x^{2} - 1344 x + 128

Expand

(x - 6 x + 5)^{7} : - 78125 x^{7} + 546875 x^{6} - 1640625 x^{5} + 2734375 x^{4} - 2734375 x^{3} + 1640625 x^{2} - 546875 x + 78125

x^{14} - 21 x^{13} + 203 x^{12} - 1197 x^{11} + 4809 x^{10} - 13923 x^{9} + 29953 x^{8} - 48639 x^{7} + 59906 x^{6} - 55692 x^{5} + 38472 x^{4} - 19152 x^{3} + 6496 x^{2} - 1344 x + 128 = - 78125 x^{7} + 546875 x^{6} - 1640625 x^{5} + 2734375 x^{4} - 2734375 x^{3} + 1640625 x^{2} - 546875 x + 78125

Subtract

- 78125 x^{7} + 546875 x^{6} - 1640625 x^{5} + 2734375 x^{4} - 2734375 x^{3} + 1640625 x^{2} - 546875 x + 78125

from both sides

x^{14} - 21 x^{13} + 203 x^{12} - 1197 x^{11} + 4809 x^{10} - 13923 x^{9} + 29953 x^{8} - 48639 x^{7} + 59906 x^{6} - 55692 x^{5} + 38472 x^{4} - 19152 x^{3} + 6496 x^{2} - 1344 x + 128 - (- 78125 x^{7} + 546875 x^{6} - 1640625 x^{5} + 2734375 x^{4} - 2734375 x^{3} + 1640625 x^{2} - 546875 x + 78125) = - 78125 x^{7} + 546875 x^{6} - 1640625 x^{5} + 2734375 x^{4} - 2734375 x^{3} + 1640625 x^{2} - 546875 x + 78125 - (- 78125 x^{7} + 546875 x^{6} - 1640625 x^{5} + 2734375 x^{4} - 2734375 x^{3} + 1640625 x^{2} - 546875 x + 78125)

Simplify

x^{14} - 21 x^{13} + 203 x^{12} - 1197 x^{11} + 4809 x^{10} - 13923 x^{9} + 29953 x^{8} + 29486 x^{7} - 486969 x^{6} + 1584933 x^{5} - 2695903 x^{4} + 2715223 x^{3} - 1634129 x^{2} + 545531 x - 77997 = 0

Factor

x^{14} - 21 x^{13} + 203 x^{12} - 1197 x^{11} + 4809 x^{10} - 13923 x^{9} + 29953 x^{8} + 29486 x^{7} - 486969 x^{6} + 1584933 x^{5} - 2695903 x^{4} + 2715223 x^{3} - 1634129 x^{2} + 545531 x - 77997 : (x - 1)^{7} (x + 3) (x^{6} - 17 x^{5} + 135 x^{4} - 685 x^{3} + 2615 x^{2} - 8517 x + 25999)

(x - 1)^{7} (x + 3) (x^{6} - 17 x^{5} + 135 x^{4} - 685 x^{3} + 2615 x^{2} - 8517 x + 25999) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x + 3 = 0 or x^{6} - 17 x^{5} + 135 x^{4} - 685 x^{3} + 2615 x^{2} - 8517 x + 25999 = 0

Solve

x - 1 = 0 : x = 1

Solve

x + 3 = 0 : x = - 3

Solve

x^{6} - 17 x^{5} + 135 x^{4} - 685 x^{3} + 2615 x^{2} - 8517 x + 25999 = 0 :

No Solution for

x \in R

The solutions are

x = 1, x = - 3

3 x^{3} - 15 x^{2} - 42 x = 0

2 x^{5} - x^{3} + 2 x^{2} = 1

m^{10} + 8 m = - 10 m - 8

x^{4} + x - 7 = 0

16 x^{3} - 16 = 0

What are the solutions to the equation (x^2-3x+2)^7=(x-6x+5)^7 ?
The solutions to the equation (x^2-3x+2)^7=(x-6x+5)^7 are x=1,x=-3
Find the zeros of (x^2-3x+2)^7=(x-6x+5)^7
The zeros of (x^2-3x+2)^7=(x-6x+5)^7 are x=1,x=-3