Solve each of the following bisquared equations : -3x^2+2=0 2^circ x^4+x^2-2=0 3^circ 4x^4-21x^2+27=0

Question

Solve each of the following bisquared equations : -3x^2+2=0 2^circ x^4+x^2-2=0 3^circ 4x^4-21x^2+27=0

Answer 1

Let's solve each of the given equations:1.

To solve this equation, we can rearrange it to isolate

:

Dividing both sides by -3:

Taking the square root of both sides:

Simplifying the square root:

Therefore, the solutions to the equation

are

and

.2.

This equation is not in a standard polynomial form. Let's rewrite it as:

To solve this equation, we can use substitution. Let

. Then the equation becomes:

This is a quadratic equation in

. We can solve it using the quadratic formula:

where

,

, and

. Plugging in these values:

Simplifying:

This gives us two solutions for

:

and

Since

, we have:

or

The first equation gives us

, and the second equation has no real solutions since the square of a real number cannot be negative.Therefore, the solutions to the equation

are

and

.3.

This equation is not in a standard polynomial form. Let's rewrite it as:

To solve this equation, we can use substitution. Let

. Then the equation becomes:

This is a quadratic equation in

. We can solve it using the quadratic formula:

where

,

, and

. Plugging in these values:

Simplifying:

This gives us two solutions for

:

and

Since

, we have:

or

Taking the square root of both sides:

or

Therefore, the solutions to the equation

are

and

.

Soru

Solve each of the following bisquared equations : -3x^2+2=0 2^circ x^4+x^2-2=0 3^circ 4x^4-21x^2+27=0

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