Question

What are the solutions of the equation 9x4-2x2-7=0? Use u substitution to solve.
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Answer 1

Answer:X=i and ±
`\sqrt{(7)/(9) }`

Explanation:

Answer 2

Answer : The solutions of the equation are,
`x=\pm i\sqrt{(7)/(9)}` and
`x=\pm 1`

Step-by-step explanation :

As we are given that the expression of equation as:

`9x^4-2x^2-7=0`

Let
`x^2=u`, we get:

`9u^2-2u-7=0`

Now split this expression by middle term splitting method.

`9u^2-9u+7u-7=0`

`9u(u-1)+7(u-1)=0`

`(9u+7)(u-1)=0`

(9u+7) = 0 and (u-1) = 0

`u=(-7)/(9)` and u = 1

As,

`x^2=u`

Thus, the value of 'x' for
`u=(-7)/(9)` is:

`x^2=u=(-7)/(9)`

`x^2=(-7)/(9)`

`x=\sqrt{(-7)/(9)}`
`(i^2=-1)`

`x=\pm i\sqrt{(7)/(9)}`

The value of 'x' for
`u=1` is:

`x^2=u=1`

`x^2=1`

`x=\pm 1`

Therefore, the solutions of the equation are,
`x=\pm i\sqrt{(7)/(9)}` and
`x=\pm 1`