What are the solutions to the equation x^5+x^{15}+x^{25}=780 ?

The solutions to the equation x^5+x^{15}+x^{25}=780 are x=\sqrt[5]{(4.66542E15)/(1.25E15)}

Find the zeros of x^5+x^{15}+x^{25}=780

The zeros of x^5+x^{15}+x^{25}=780 are x=\sqrt[5]{(4.66542E15)/(1.25E15)}

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x^{5} + x^{15} + x^{25} = 780

Decimal Notation

x = 1.30135 \dots

Solution steps

x^{5} + x^{15} + x^{25} = 780

Move

780

to the left side

x^{5} + x^{15} + x^{25} - 780 = 0

Write in the standard form

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

x^{25} + x^{15} + x^{5} - 780 = 0

Rewrite the equation with

u = x^{5}, u^{3} = x^{15}

and

u^{5} = x^{25}

u^{5} + u^{3} + u - 780 = 0

Solve

u^{5} + u^{3} + u - 780 = 0 : u \approx 3.73233 \dots

u \approx 3.73233 \dots

Substitute back

u = x^{5},

solve for

x

Solve

The solution is

9 x^{4} - 42 x^{3} + 64 x^{2} - 35 x + 4 = 0

z^{4} = 4 i

r^{3} - 5 r^{2} + 8 r - 4 = 0

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

x^{3} - 6 x + 9 = 0

What are the solutions to the equation x^5+x^{15}+x^{25}=780 ?
The solutions to the equation x^5+x^{15}+x^{25}=780 are x=\sqrt[5]{(4.66542E15)/(1.25E15)}
Find the zeros of x^5+x^{15}+x^{25}=780
The zeros of x^5+x^{15}+x^{25}=780 are x=\sqrt[5]{(4.66542E15)/(1.25E15)}