Question

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

Answer 1

Answer:X=i and ±$\sqrt{\frac{7}{9} }$

Step-by-step explanation:

Answer 2

Answer : The solutions of the equation are, $x=\pm i\sqrt{\frac{7}{9}}$ 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

$u=\frac{-7}{9}$ and u = 1

As,

$x^2=u$

Thus, the value of 'x' for $u=\frac{-7}{9}$ is:

$x^2=u=\frac{-7}{9}$

$x^2=\frac{-7}{9}$

$x=\sqrt{\frac{-7}{9}}$        $(i^2=-1)$

$x=\pm i\sqrt{\frac{7}{9}}$

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, $x=\pm i\sqrt{\frac{7}{9}}$ and $x=\pm 1$