What are the solutions to the equation x^6-28x+27=0 ?

The solutions to the equation x^6-28x+27=0 are x=1,x\approx 1.62716…

Find the zeros of x^6-28x+27=0

The zeros of x^6-28x+27=0 are x=1,x\approx 1.62716…

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x^{6} - 28 x + 27 = 0

x = 1, x \approx 1.62716 \dots

Solution steps

x^{6} - 28 x + 27 = 0

Factor

x^{6} - 28 x + 27 : (x - 1) (x^{5} + x^{4} + x^{3} + x^{2} + x - 27)

(x - 1) (x^{5} + x^{4} + x^{3} + x^{2} + x - 27) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{5} + x^{4} + x^{3} + x^{2} + x - 27 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{5} + x^{4} + x^{3} + x^{2} + x - 27 = 0 : x \approx 1.62716 \dots

The solutions are

x = 1, x \approx 1.62716 \dots

x^{4} - 16 x^{2} + 63 = 0

x^{3} - 15 x + 1 = 0

x, x^{3} + y^{5} = 4

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

m^{4} + 7 m^{2} + 6 = 0

What are the solutions to the equation x^6-28x+27=0 ?
The solutions to the equation x^6-28x+27=0 are x=1,x\approx 1.62716…
Find the zeros of x^6-28x+27=0
The zeros of x^6-28x+27=0 are x=1,x\approx 1.62716…