What are the solutions to the equation (x-3)^7=64(x-3)^4 ?

The solutions to the equation (x-3)^7=64(x-3)^4 are x=3,x=7,x=1+2sqrt(3)i,x=1-2sqrt(3)i

Find the zeros of (x-3)^7=64(x-3)^4

The zeros of (x-3)^7=64(x-3)^4 are x=3,x=7,x=1+2sqrt(3)i,x=1-2sqrt(3)i

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(x - 3)^{7} = 64 (x - 3)^{4}

x = 3, x = 7, x = 1 + 23 i, x = 1 - 23 i

Solution steps

(x - 3)^{7} = 64 (x - 3)^{4}

Expand

(x - 3)^{7} : x^{7} - 21 x^{6} + 189 x^{5} - 945 x^{4} + 2835 x^{3} - 5103 x^{2} + 5103 x - 2187

Expand

64 (x - 3)^{4} : 64 x^{4} - 768 x^{3} + 3456 x^{2} - 6912 x + 5184

x^{7} - 21 x^{6} + 189 x^{5} - 945 x^{4} + 2835 x^{3} - 5103 x^{2} + 5103 x - 2187 = 64 x^{4} - 768 x^{3} + 3456 x^{2} - 6912 x + 5184

Subtract

64 x^{4} - 768 x^{3} + 3456 x^{2} - 6912 x + 5184

from both sides

x^{7} - 21 x^{6} + 189 x^{5} - 945 x^{4} + 2835 x^{3} - 5103 x^{2} + 5103 x - 2187 - (64 x^{4} - 768 x^{3} + 3456 x^{2} - 6912 x + 5184) = 64 x^{4} - 768 x^{3} + 3456 x^{2} - 6912 x + 5184 - (64 x^{4} - 768 x^{3} + 3456 x^{2} - 6912 x + 5184)

Simplify

x^{7} - 21 x^{6} + 189 x^{5} - 1009 x^{4} + 3603 x^{3} - 8559 x^{2} + 12015 x - 7371 = 0

Factor

x^{7} - 21 x^{6} + 189 x^{5} - 1009 x^{4} + 3603 x^{3} - 8559 x^{2} + 12015 x - 7371 : (x - 3)^{4} (x - 7) (x^{2} - 2 x + 13)

(x - 3)^{4} (x - 7) (x^{2} - 2 x + 13) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x - 7 = 0 or x^{2} - 2 x + 13 = 0

Solve

x - 3 = 0 : x = 3

Solve

x - 7 = 0 : x = 7

Solve

x^{2} - 2 x + 13 = 0 : x = 1 + 23 i, x = 1 - 23 i

The solutions are

x = 3, x = 7, x = 1 + 23 i, x = 1 - 23 i

- 16 y - y^{3} + 32 = 0

x^{3} - 3 = - 30

(x - 1) (x - 2) (x + 1) = 0

8 t^{3} + 2 = 66

2 x^{3} - 5 x^{2} + 4 x - 10 = 0

What are the solutions to the equation (x-3)^7=64(x-3)^4 ?
The solutions to the equation (x-3)^7=64(x-3)^4 are x=3,x=7,x=1+2sqrt(3)i,x=1-2sqrt(3)i
Find the zeros of (x-3)^7=64(x-3)^4
The zeros of (x-3)^7=64(x-3)^4 are x=3,x=7,x=1+2sqrt(3)i,x=1-2sqrt(3)i