What are the solutions to the equation 9x^4=25x^2-16 ?

The solutions to the equation 9x^4=25x^2-16 are x= 4/3 ,x=-4/3 ,x=1,x=-1

Find the zeros of 9x^4=25x^2-16

The zeros of 9x^4=25x^2-16 are x= 4/3 ,x=-4/3 ,x=1,x=-1

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9 x^{4} = 25 x^{2} - 16

x = \frac{4}{3}, x = - \frac{4}{3}, x = 1, x = - 1

Decimal Notation

x = 1.33333 \dots, x = - 1.33333 \dots, x = 1, x = - 1

Solution steps

9 x^{4} = 25 x^{2} - 16

Move

16

to the left side

9 x^{4} + 16 = 25 x^{2}

Move

25 x^{2}

to the left side

9 x^{4} + 16 - 25 x^{2} = 0

Write in the standard form

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

9 x^{4} - 25 x^{2} + 16 = 0

Rewrite the equation with

u = x^{2}

and

u^{2} = x^{4}

9 u^{2} - 25 u + 16 = 0

Solve

9 u^{2} - 25 u + 16 = 0 : u = \frac{16}{9}, u = 1

u = \frac{16}{9}, u = 1

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = \frac{16}{9} : x = \frac{4}{3}, x = - \frac{4}{3}

Solve

x^{2} = 1 : x = 1, x = - 1

The solutions are

x = \frac{4}{3}, x = - \frac{4}{3}, x = 1, x = - 1

x, x^{3} + y^{3} - z^{3} = 4

x^{3} - 2 x - 5 = 0, (x = 2.0813)

(x - \frac{1}{3}) (x^{2} + x \frac{0.1}{3} + \frac{1 ^{2}}{3 ^{2}}) = 64

(x - 7)^{4} = (x - 7)^{5}

x^{3} = - 125

What are the solutions to the equation 9x^4=25x^2-16 ?
The solutions to the equation 9x^4=25x^2-16 are x= 4/3 ,x=-4/3 ,x=1,x=-1
Find the zeros of 9x^4=25x^2-16
The zeros of 9x^4=25x^2-16 are x= 4/3 ,x=-4/3 ,x=1,x=-1