x^4 + 2x^2 - 10 = 0 (HINT: let x^2 = z)?

Question

please show me how you get the answer!
thank you!

Answer 1

if you let x^2 = z, the equation would be written as follows:

z^2 + 2z - 10 = 0

using quadratic formula [-b + or - sqrt(b^2 - 4ac)]/2a
and a=1; b=2; c = -10
z = [-2 +or- sqrt(44)]/ 2

since x^2 = z, if you take the square root of that whole thing, (including +or- at the front), you would get x
there would be 4 possible answers for x since you have the plus or minus in what z equals and then taking the square root you get another plus or minus

Answer 2

Use quadratic formula directly for x^2:
x^2 = -1+√11
x = ±√( -1+√11)

Answer 3

z ² + 2z - 10 = 0
z = [ - 2 ± √(4 + 40) ] / 2
z = [- 2 ± √(44) ] / 2
z = [- 2 ± 2√(11)] / 2
z = [ - 1 ± √(11) ]
x ² = [ - 1 ± √(11) ]
x = ± [ - 1 ± √(11)] ^(1/2)

Answer 4

Yes, use your hint.

z^2 + 2z - 10 = 0

The quadratic formula gives the roots:

z = -1 +/- sqrt(11)

x = sqrt(z) = sqrt(sqrt(11) -1), -sqrt(sqrt(11) -1), isqrt(sqrt(11) + 1), and -isqrt(sqrt(11) + 1), where i = sqrt(-1)

Answer 5

using formula then x ² =[-b±√(b²-4ac)] /(2a)]
x ² = 2.3166 or x ² = - 4.3166
then x = 1.522 or -1.522 or i2.078 or - i2.078 where i =√-1