Question

Show that the equation x^3+4x=6 has a solution between 1.1 and 1.2

Answer 1

Answer:

see explanation

Step-by-step explanation:

If there is a solution between x = 1.1 and x = 1.2 then there will be a change in sign when the equation is evaluated at the points, indicating the graph has crossed the x- axis, where the solution lies.

Given

x³ + 4x = 6 ( subtract 6 from both sides )

x³ + 4x - 6 = 0 ← in standard form

Evaluating for x = 1.1

(1.1)³ + 4(1.1) - 6

= 1.331 + 4.4 - 6 = - 0.269 ← < 0

Evaluating for x = 1.2

(1.2)³ + 4(1.2) - 6

= 1.728 + 4.8 - 6 = 0.528 ← > 0

Since there is a change in sign the graph has crossed the x-axis from below /   indicating a solution between x = 1.1 and x = 1.2