What are the solutions to the equation (x-1.5)^6+2(1.5-x)^2=0 ?

The solutions to the equation (x-1.5)^6+2(1.5-x)^2=0 are x=1.5

Find the zeros of (x-1.5)^6+2(1.5-x)^2=0

The zeros of (x-1.5)^6+2(1.5-x)^2=0 are x=1.5

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(x - 1.5)^{6} + 2 (1.5 - x)^{2} = 0

x = 1.5

Solution steps

(x - 1.5)^{6} + 2 (1.5 - x)^{2} = 0

Factor

(x - 1.5)^{6} + 2 (1.5 - x)^{2} : (x - 1.5)^{2} (x^{4} - 6 x^{3} + \frac{27 x ^{2}}{2} - 13.5 x + 7.0625)

(x - 1.5)^{2} (x^{4} - 6 x^{3} + \frac{27 x ^{2}}{2} - 13.5 x + 7.0625) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1.5 = 0 or x^{4} - 6 x^{3} + \frac{27 x ^{2}}{2} - 13.5 x + 7.0625 = 0

Solve

x - 1.5 = 0 : x = 1.5

Solve

x^{4} - 6 x^{3} + \frac{27 x ^{2}}{2} - 13.5 x + 7.0625 = 0 :

No Solution for

x \in R

The solution is

x = 1.5

12 x^{3} - 17 x^{2} + 20 x + 4 = 0

x^{8} - 15 x^{4} - 16 = 0

36 f^{3} = 121 f

- 2 x^{4} + 7 = 2 x + 5

(x + 1) (2 x - 1)^{2} = 1

What are the solutions to the equation (x-1.5)^6+2(1.5-x)^2=0 ?
The solutions to the equation (x-1.5)^6+2(1.5-x)^2=0 are x=1.5
Find the zeros of (x-1.5)^6+2(1.5-x)^2=0
The zeros of (x-1.5)^6+2(1.5-x)^2=0 are x=1.5