What are the solutions to the equation 5(y-3)^6-13(y-3)^4-6(y-3)^2=0 ?

The solutions to the equation 5(y-3)^6-13(y-3)^4-6(y-3)^2=0 are y=3,y=-sqrt(3)+3,y=sqrt(3)+3

Find the zeros of 5(y-3)^6-13(y-3)^4-6(y-3)^2=0

The zeros of 5(y-3)^6-13(y-3)^4-6(y-3)^2=0 are y=3,y=-sqrt(3)+3,y=sqrt(3)+3

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5 (y - 3)^{6} - 13 (y - 3)^{4} - 6 (y - 3)^{2} = 0

y = 3, y = - 3 + 3, y = 3 + 3

Decimal Notation

y = 3, y = 1.26794 \dots, y = 4.73205 \dots

Solution steps

5 (y - 3)^{6} - 13 (y - 3)^{4} - 6 (y - 3)^{2} = 0

Factor

5 (y - 3)^{6} - 13 (y - 3)^{4} - 6 (y - 3)^{2} : (y - 3)^{2} (5 y^{4} - 60 y^{3} + 257 y^{2} - 462 y + 282)

(y - 3)^{2} (5 y^{4} - 60 y^{3} + 257 y^{2} - 462 y + 282) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y - 3 = 0 or 5 y^{4} - 60 y^{3} + 257 y^{2} - 462 y + 282 = 0

Solve

y - 3 = 0 : y = 3

Solve

5 y^{4} - 60 y^{3} + 257 y^{2} - 462 y + 282 = 0 : y = - 3 + 3, y = 3 + 3

The solutions are

y = 3, y = - 3 + 3, y = 3 + 3

x^{3} - 5 = 0

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

x^{3} + x - 10 = 0

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

m^{3} + 8 = 0

What are the solutions to the equation 5(y-3)^6-13(y-3)^4-6(y-3)^2=0 ?
The solutions to the equation 5(y-3)^6-13(y-3)^4-6(y-3)^2=0 are y=3,y=-sqrt(3)+3,y=sqrt(3)+3
Find the zeros of 5(y-3)^6-13(y-3)^4-6(y-3)^2=0
The zeros of 5(y-3)^6-13(y-3)^4-6(y-3)^2=0 are y=3,y=-sqrt(3)+3,y=sqrt(3)+3