What are the solutions to the equation (x-5)^7=(x-5)^9 ?

The solutions to the equation (x-5)^7=(x-5)^9 are x=4,x=5,x=6

Find the zeros of (x-5)^7=(x-5)^9

The zeros of (x-5)^7=(x-5)^9 are x=4,x=5,x=6

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(x - 5)^{7} = (x - 5)^{9}

x = 4, x = 5, x = 6

Solution steps

(x - 5)^{7} = (x - 5)^{9}

Expand

(x - 5)^{7} : x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125

Expand

(x - 5)^{9} : x^{9} - 45 x^{8} + 900 x^{7} - 10500 x^{6} + 78750 x^{5} - 393750 x^{4} + 1312500 x^{3} - 2812500 x^{2} + 3515625 x - 1953125

x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125 = x^{9} - 45 x^{8} + 900 x^{7} - 10500 x^{6} + 78750 x^{5} - 393750 x^{4} + 1312500 x^{3} - 2812500 x^{2} + 3515625 x - 1953125

Switch sides

x^{9} - 45 x^{8} + 900 x^{7} - 10500 x^{6} + 78750 x^{5} - 393750 x^{4} + 1312500 x^{3} - 2812500 x^{2} + 3515625 x - 1953125 = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125

Subtract

x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125

from both sides

x^{9} - 45 x^{8} + 900 x^{7} - 10500 x^{6} + 78750 x^{5} - 393750 x^{4} + 1312500 x^{3} - 2812500 x^{2} + 3515625 x - 1953125 - (x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125) = x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125 - (x^{7} - 35 x^{6} + 525 x^{5} - 4375 x^{4} + 21875 x^{3} - 65625 x^{2} + 109375 x - 78125)

Simplify

x^{9} - 45 x^{8} + 899 x^{7} - 10465 x^{6} + 78225 x^{5} - 389375 x^{4} + 1290625 x^{3} - 2746875 x^{2} + 3406250 x - 1875000 = 0

Factor

x^{9} - 45 x^{8} + 899 x^{7} - 10465 x^{6} + 78225 x^{5} - 389375 x^{4} + 1290625 x^{3} - 2746875 x^{2} + 3406250 x - 1875000 : (x - 4) (x - 5)^{7} (x - 6)

(x - 4) (x - 5)^{7} (x - 6) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x - 5 = 0 or x - 6 = 0

Solve

x - 4 = 0 : x = 4

Solve

x - 5 = 0 : x = 5

Solve

x - 6 = 0 : x = 6

The solutions are

x = 4, x = 5, x = 6

y, x = 4 - (y + 3)^{5}

2 - 6 x + 8 x^{2} - 2 x^{3} = 4 x - 2

u^{3} = - 18

x^{4} - 4 x^{2} - 77 = 0

((x - 2)^{2})^{2} - 2 (x - 2)^{2} = 0

What are the solutions to the equation (x-5)^7=(x-5)^9 ?
The solutions to the equation (x-5)^7=(x-5)^9 are x=4,x=5,x=6
Find the zeros of (x-5)^7=(x-5)^9
The zeros of (x-5)^7=(x-5)^9 are x=4,x=5,x=6