Check the solution to "Solve each equation. 9x4−37x2+4=0"

osula9a

Answered question

2021-12-17

Solve each equation.

9 x^{4} - 37 x^{2} + 4 = 0

Shannon Hodgkinson

Beginner2021-12-18Added 34 answers

Step 1
The given equation is,

9 x^{4} - 37 x^{2} + 4 = 0

To find the solution of the given equation, we use the factorization method.
Step 2
Using the factorization method,

9 x^{4} - 37 x^{2} + 4 = 0

9 x^{4} - 36 x^{2} - x^{2} + 4 = 0

9 x^{2} (x^{2} - 4) - 1 (x^{2} - 4) = 0

(9 x^{2} - 1) (x^{2} - 4) = 0

Now,

9 x^{2} - 1 = 0

9 x^{2} = 1

x^{2} = \frac{1}{9}

x = \pm \frac{1}{3}

and,

x^{2} - 4 = 0

x^{2} = 4

x = \pm 2

Therefore, the solutions of the given equation are as, -2,

- \frac{1}{3}, \frac{1}{3}

and 2

sonorous9n

Beginner2021-12-19Added 34 answers

Given expression is

9 x^{4} - 37 x^{2} + 4 = 0

9 {(x^{2})}^{2} - 37 {(x)}^{2} + 4 = 0

A quadratic equation written in the form

a x^{2} + b x + c = 0

has the solutions

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Here a=9, b=-37 and c=4
Therefore

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

x^{2} = \frac{- (- 37) \pm \sqrt{{(- 37)}^{2} - 4 (9) (4)}}{2 (9)}

= \frac{37 \pm \sqrt{1369 - 144}}{18}

= \frac{37 \pm 35}{18}

x^{2} = \frac{72}{18}

x^{2} = \frac{2}{18}

x^{2} = 4

x^{2} = \frac{1}{9}

x = \pm 2

x = \pm \frac{1}{3}

The solutions are

\pm 2

and

\pm \frac{1}{3}

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