X^4-4x^2+3=0? i really don't know what to do.?

Question

the answer is ± √3 and ± 1

Answer 1

Substitute y for x^2. That way it becomes

y^2 - 4y + 3 = 0

Factor it...

(y-3)(y-1)=0

y = 3 , 1

But you have to solve for x...

y=x^2

x^2 = 3

x^2 = 1

Take the square root fo both sides

x = ± √3

x = ± 1

Answer 2

you can solve by factoring or by chunking.

Factoring :

( x^2 - 3) (x^2 - 1) = 0

Using the zero product property :

x^2 = 3   OR x^2 = 1

Take the square root of both sides, which means to insert the ±

and you get x = ± √3  OR x = ± 1

Good luck to you !!

Answer 3

x⁴-4x²+3=0

subst y = x²

y² - 4y + 3 = 0

(y - 3)(y - 1) = 0

put back the x²

(x² - 3)(x² - 1) = 0

factor

(x + √3)(x - √3)(x + 1)(x - 1) = 0

x = ±√3, ±1

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