What are the solutions to the equation (x-3)^4-3(x-3)^2-10=0 ?

The solutions to the equation (x-3)^4-3(x-3)^2-10=0 are x=-sqrt(5)+3,x=sqrt(5)+3

Find the zeros of (x-3)^4-3(x-3)^2-10=0

The zeros of (x-3)^4-3(x-3)^2-10=0 are x=-sqrt(5)+3,x=sqrt(5)+3

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(x - 3)^{4} - 3 (x - 3)^{2} - 10 = 0

x = - 5 + 3, x = 5 + 3

Decimal Notation

x = 0.76393 \dots, x = 5.23606 \dots

Solution steps

(x - 3)^{4} - 3 (x - 3)^{2} - 10 = 0

Expand

(x - 3)^{4} - 3 (x - 3)^{2} - 10 : x^{4} - 12 x^{3} + 51 x^{2} - 90 x + 44

x^{4} - 12 x^{3} + 51 x^{2} - 90 x + 44 = 0

Find one solution for

x^{4} - 12 x^{3} + 51 x^{2} - 90 x + 44 = 0

using Newton-Raphson:

x \approx 0.76393 \dots

Apply long division:

\frac{x ^{4} - 12 x ^{3} + 51 x ^{2} - 90 x + 44}{x - 0.76393 \dots} = x^{3} - 11.23606 \dots x^{2} + 42.41640 \dots x - 57.59674 \dots

x^{3} - 11.23606 \dots x^{2} + 42.41640 \dots x - 57.59674 \dots \approx 0

Find one solution for

x^{3} - 11.23606 \dots x^{2} + 42.41640 \dots x - 57.59674 \dots = 0

using Newton-Raphson:

x \approx 5.23606 \dots

Apply long division:

\frac{x ^{3} - 11.23606 \dots x ^{2} + 42.41640 \dots x - 57.59674 \dots}{x - 5.23606 \dots} = x^{2} - 6 x + 11

x^{2} - 6 x + 11 \approx 0

Find one solution for

x^{2} - 6 x + 11 = 0

using Newton-Raphson:

No Solution for

x \in R

Approximate to algebraic form

x \approx 0.76393 \dots : x = - 5 + 3

x \approx 5.23606 \dots : x = 5 + 3

x = - 5 + 3, x = 5 + 3

The solutions are

x = - 5 + 3, x = 5 + 3

240 t - 60 t^{3} = 0

y, x = y^{9}

x^{5} + 15 x + 62 = 0

20 x^{3} + 12 x^{2} - 5 x - 3 = 0

x^{4} - 10 x^{3} + 120 x + 144 = 0

What are the solutions to the equation (x-3)^4-3(x-3)^2-10=0 ?
The solutions to the equation (x-3)^4-3(x-3)^2-10=0 are x=-sqrt(5)+3,x=sqrt(5)+3
Find the zeros of (x-3)^4-3(x-3)^2-10=0
The zeros of (x-3)^4-3(x-3)^2-10=0 are x=-sqrt(5)+3,x=sqrt(5)+3