Question

solve (x³+x²+x+1)(x-1)/(x⁴-4)≥0 (linear inequality)

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept

When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this comparison is known as a linear inequality since at least one linear algebraic expression is involved. It's important to remember that if p q, then p must be a number that is unambiguously less than q. If p q, then p is a number that is strictly smaller than q or exactly equal to q. The same is true for the final two inequality signs > (greater than) and (greater than or equal to).

Given

the expression is (x³+x²+x+1)(x-1)/(x⁴-4)≥0

Find

we need to solve the above expression.

Solution

(x³+x²+x+1)(x-1)/(x⁴-4)≥0

x(x³+x²+x+1)₋(1)(x³+x²+x+1)/(x⁴-4)≥0

x⁴₊x³₊x²₊x₋x³₋x²₋x₋1/(x⁴-4)≥0

x⁴₋1/x⁴₋4≥0

x⁴₋1≥0

x⁴₋1 = 0

x⁴ = 1

x = 1

Therefore after solving the inequality we get the answer as x = 1.

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