Question

If x > 0, prove that x³ + 7x + 1 > 3x²

Restricted solving by

1 Graph
2 Substituting x-values.

Answer 1

If x > 0 is prove that x³ + 7x + 1 > 3x²

Step-by-step explanation:

To prove this inequality, we can start by expanding the left-hand side of the equation:

x³ + 7x + 1 = (x + 1)(x + 2)(x + 3) + 7x

Since x is positive, we can use the fact that (a + b)(a + c) ≥ ac + bc for any positive a, b, and c to simplify the expression:

x³ + 7x + 1 ≥ (x + 1)(x + 2) + 7x

Now, we can see that the first two factors on the left-hand side are all greater than or equal to 0, so we can drop the inequality sign and simplify further:

x³ + 7x + 1 ≥ 0

Finally, we can factor out the x² term to get:

x³ + 7x + 1 > 3x²