What are the solutions to the equation (x-15)^6+2(15-x)^2=0 ?

The solutions to the equation (x-15)^6+2(15-x)^2=0 are x=15

Find the zeros of (x-15)^6+2(15-x)^2=0

The zeros of (x-15)^6+2(15-x)^2=0 are x=15

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(x - 15)^{6} + 2 (15 - x)^{2} = 0

x = 15

Solution steps

(x - 15)^{6} + 2 (15 - x)^{2} = 0

Factor

(x - 15)^{6} + 2 (15 - x)^{2} : (x - 15)^{2} (x^{4} - 60 x^{3} + 1350 x^{2} - 13500 x + 50627)

(x - 15)^{2} (x^{4} - 60 x^{3} + 1350 x^{2} - 13500 x + 50627) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 15 = 0 or x^{4} - 60 x^{3} + 1350 x^{2} - 13500 x + 50627 = 0

Solve

x - 15 = 0 : x = 15

Solve

x^{4} - 60 x^{3} + 1350 x^{2} - 13500 x + 50627 = 0 :

No Solution for

x \in R

The solution is

x = 15

- x^{3} + 11 x^{2} - 39 x + 45 = 0

x^{3} - 3 x^{2} + 25 x - 75 = 0

y, x = (y^{3} + 7)^{6}

x^{5} - 6 x^{2} = 0

x^{3} + 9 = 0

What are the solutions to the equation (x-15)^6+2(15-x)^2=0 ?
The solutions to the equation (x-15)^6+2(15-x)^2=0 are x=15
Find the zeros of (x-15)^6+2(15-x)^2=0
The zeros of (x-15)^6+2(15-x)^2=0 are x=15