Question

find the solution of
x^4-×^2-1<0​

Answer 1

Step-by-step explanation:

Four solutions were found :

x =√-0.618 = 0.0 - 0.78615 i

x =√-0.618 = 0.0 + 0.78615 i

x =√ 1.618 = -1.27202

x =√ 1.618 = 1.27202

Step by step solution :

Step 1 :

Trying to factor by splitting the middle term

1.1 Factoring x4-x2-1

The first term is, x4 its coefficient is 1 .

The middle term is, -x2 its coefficient is -1 .

The last term, "the constant", is -1

Step-1 : Multiply the coefficient of the first term by the constant 1 • -1 = -1

Step-2 : Find two factors of -1 whose sum equals the coefficient of the middle term, which is -1 .

-1 + 1 = 0

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 1 :

x4 - x2 - 1 = 0

Step 2 :

Solving a Single Variable Equation :

Equations which are reducible to quadratic :

2.1 Solve x4-x2-1 = 0

This equation is reducible to quadratic. What this means is that using a new variable, we can rewrite this equation as a quadratic equation Using w , such that w = x2 transforms the equation into :

w2-w-1 = 0

Solving this new equation using the quadratic formula we get two real solutions :

1.6180 or -0.6180

Now that we know the value(s) of w , we can calculate x since x is √ w

Doing just this we discover that the solutions of

x4-x2-1 = 0

are either :

x =√ 1.618 = 1.27202 or :

x =√ 1.618 = -1.27202 or :

x =√-0.618 = 0.0 + 0.78615 i or :

x =√-0.618 = 0.0 - 0.78615 i